life changing quadratic formula

[@madomation7984]

During a math class, I accidently derived this method from scratch, I thought that this is a new method that no one knew, then realised this is the derivation of the quadratic formula that we were just not taught.

[@soumyadwipmondal2222]

Same bro!

[@aparnarai3708]

@@epc0003 it's quite possible Sometimes you just don't wanna go with the said method and try your best to find another way to achieve the answer One does not need to be Po- Shen Lo to come up with this

[@vanshkhatri8233]

I also derived the formula during my class and showed to my teacher but he said " the book does not say so and I'll deduct your marks if u use the".... nvm I am so happy now that I was correct

[@pradness]

@@epc0003 fr, it's really hard to derive this method from scratch as a student, how would someone come up with taking the midpoint of roots then using it as being equidistant from roots and calculating that distance to calculate roots, I always wondered why addition of roots and multiplication of roots was so easy compared to the quadratic formula but I would never imagine myself deriving this

[@e_pi_i_is_-1]

@@vanshkhatri8233 lmao, this actually happened with me.

[@mimithehotdog7836]

“Modern Problems Require Ancient Methods”

[@edgardojaviercanu4740]

a wonderful concept.

[@rahulrathod6770]

Absolutely right

[@hozesty]

E C 100%

[@jewzetto9492]

Ironic but sometimes true

[@trubobu]

Haha ancient chisel go brrr

[@ac281201]

When you simplify all the steps taken, it turns out that the _u_ is actually equal to √∆/2a, so this is quadratic formula but in multiple steps instead of single equation.

I just came to the same conclusion. This method basically derives the quadratic formula from "graphical" solution. Which I think, is actually quite educational.

[@leonardokeller5254]

My mathteacher used this “method”, well it’s actually common sense if you think it through, to explain us the abc formula

[@johnspence8141]

Yes of course. It’s not going to miraculously break away. But it is definitely an easier way to conceptualize the process. Most students just memorize the quadratic function instead of deriving it. Whereas this method fits nicely into the same method applied to whole number roots. Every student I’ve taught who just memorized formulas deprived themselves of seeing all the connections in math and as a result never become really good at math.

[@mathsman5219]

Perspective changed

[@johnholmes912]

@@johnspence8141 isn't the easiest way to just complete the square?

[@shabbarvejlani]

Can relate the formula for roots more intuitively now. MID = -b/2a U= sqrt(b^2 - 4ac)/2a X1 = MID + U X2 = MID - U Thanks for sharing this.

[@yeet6074]

Hey, thanks for compiling this!!

[@pinkex6119]

thanks for comenting us ew

[@itsankur8745]

Its all fun and games until the roots are imaginary.

[@nexlord2036]

Lol

[@Amish0123]

do watch the video till end..he took that too!

[@akul2986]

@Guitarzen oh no😭

[@dororthyruth3045]

Make sure you are solving real problems

[@pafauk361]

Make sure you watch the video before you comment? Complex numbers change nothing

[@bigbro5089]

All things aside, Dr.Peyam seems to be so good of heart. He seems to be a sweet,simple and composed person 💙.... People like him change the bad inside of a person and fill them with positivity 😎💞

[@sohilkumar1218]

My thoughts exactly 😀

[@HypnosisBear]

What?

[@blackpenredpen]

Ah!

[@bryantrandolph4693]

My math teacher is here too

[@amitavadass]

My inspiration is here too!!!!

[@spandanbarve1066]

Hii

[@konradkos1981]

Legend

[@TheRealThe]

L e g e n d

[@mullaert]

Called the pq-formula. Used for students in German school who don’t want to use the quadric formula. The approach to explain the method is nicely done in this video. I really liked it.

[@NotBroihon]

Ja man pq Formel Gang amk

[@mxchronos3642]

@@NotBroihon vallah☝🏻

[@livaja27]

​@@mxchronos3642Jesus loves YOU. He died so YOU can have an eternal life in heaven. True joy, life love, peace and fulfilment is found in God. REPENT of your sins & TURN TO CHRIST 🧡 Accept Him as Lord and Saviour and be saved. Btw, I'm not a bot. There is a person behind their screen praying for you and wishing you joy and heaven that only God can give.

[@tomn.9987]

I find the quadratic formula in it's common version more practical. It's easy to remember and use.

[@RorychattInc]

As russians we were taught this in like 5th grade. We call this формула Виета (Vieta's formulas), as they exist not only for quadratic equations UPD: yes, you can use them for cubic too

[@mathadventuress]

oh so you can use them for cubic?

[@aryadebchatterjee5028]

@@mathadventuress yupp

[@aryadebchatterjee5028]

@@mathadventuress The formula states that for any equation of degree N which has roots A_i where i={1,2,3...} the sum of the roots is the coefficient of the term which has N-1 as power divided by the coefficient of the term which has Nth power TIMES -1... and just like this when the roots are taken two at a time and multiplied and then added like a series (to clear things up e.g (A1*A2)+(A2*A3)+(A3*A4)+....+(A_N-1 *A_N) )IS JUST THE THIRD COEFFICIENT divided by the the first one and and like so on I would suggest you to look it up on some good book like Hall and knight

[@DRMath]

I learned it in 6th grade, and my teacher use to say if you want to learn math or science learn from Russian and one of my professor (one of the smartest person i met in my life yet)here is US proved it.

[@prakasharyal4283]

@@aryadebchatterjee5028 great

[@xy9439]

I call this "completing the square" in a fancy way

[@aditya2781]

🙂🙂🤣🤣

[@RedRad1990]

The equations at the beginning are called Vieta's formulas

[@ruanlslima]

I call it "Bhaskara formula with geometrical intuition" hahaha Completing the square is my go-to though

[@richardfredlund3802]

completing the square doesn't use symmetry in the same way. This is slightly different.

[@LeoBrooks03]

Yes, this is essentially finding a turning point and completing the square.

[@subhojitchatterjee9920]

Teacher : This is the simplest method. Middle term factor : "I don't even exist"

[@adityagarg9988]

Westerners be like: that's cheating😭😭

[@adityagarg9988]

x^2 - 9 = 0 : idk😂😂

[@LLT_MATHEMATICAL_FLUID]

The name of the formula is middle term factor, so by its name you have to factories the middle term coefficient of the given equation by the help of initial and terminal terms. Here( -6) is the middle term coefficient and -6 = (-4)+(-2) . ( where { -4}×{ -2}= 8). So the Answer will be (x-4) (x-2).

[@subhojitchatterjee9920]

@@LLT_MATHEMATICAL_FLUID kehna kya chahte ho??

[@HarshHit]

@@adityagarg9988 x=+-3

[@deltaman2283]

You're an incredible maths teacher and a human. We need more people like you sir. You're so cheerful. You earned a subscriber here...keep uploading interesting mathematics stuffs here...love your content. I'm gonna use this method for quick solving in MCQs. Lot's of love and respect from the world. Thankyou very much for this valuable information.

[@leickrobinson5186]

If **Dr. Peyam** says that he’s the nicest guy he ever met, that’s really saying something!!!

[@KokeBeast23]

Truly!

[@abderzakchebbi1339]

yes, because probably the professor taught him something new.

[@aryamannsrivastava7279]

Gay??

[@abderzakchebbi1339]

@@aryamannsrivastava7279 no!...we cnnot juge like every nice person is gay thats very wrong...instead in general poeple with a higher education like him are nice bc their are not in the level of juck kids who are looking for trouble or bulliying instead of mind themselves.

[@aryamannsrivastava7279]

@@abderzakchebbi1339 I am sorry for my words .actually I myself found sir to be very useful and informative

[@angelicbeast]

Peyam you kept me interested in math! You were my gsi for math 54 back at Berkeley. Since then I didn't continue past abstract algebra but I still love math and I love this channel!

[@drpeyam]

Ooooooh I remember you!!! Hope all is well 😁

[@mattpyth5151]

Actually after watching Prof. Loh's video, I tried to solve one problem myself. I used an odd coeff in the middle term to have fraction solving and to my amazement, it works! Now, I am excited to teach this to my students! :)

[@drpeyam]

Wonderful!!! :)

[@remopellegrino8961]

If every math teacher was as cheerful as you, everyone would understand math!

[@tmjcbs]

Cheerfulness has very little influence on understanding math...

[@remopellegrino8961]

@@tmjcbs it makes your audience be more interested, hence they will be more focussed and they will learn a lot more

[@teddylandefeld6380]

I didn’t understand shit from this vid

[@amigosdocarro4600]

@@tmjcbs No

[@centralprocessingunit2564]

@Nawfal. wns excuses. enthusiasm of the teacher doesnt matter. the actual content is more important. if enthusiasm has an effect on a student then thats just because that student is lazy and doesnt want to do the hard work part on their own.

[@zaheerkhan9236]

Imagine someone considering this a scientific breakthrough and u applied it on high-school maths on a daily basis

[@kumnalkhati2243]

Lol

[@Suvadip1234]

True😂

[@gouharmaquboolnitp]

You are a unacademian?

[@gouharmaquboolnitp]

Ashwani Tyagi's students right?

[@x0cx102]

search up po shen loh. He does a lot more real mathematics research (in graph theory and combinatorics) as a professor at carnegie mellon, as well as coach the usa IMO team. this is hardly a breakthrough or a new method in any means. not sure why he's calling it that.

[@PrinceZuko]

If every teacher in Austria's art school back then was as cheerful as you, the world might potentially be a better place.

[@TheChaosBeat]

Lol

[@accidentallyaj5138]

This is a very specific joke, i am surprised people got this

[@obyvatel]

Ever heard of being cheerfully refused admission?

[@brittonporter5063]

Is this a Hitler joke? Just want to make sure I’m right

[@accidentallyaj5138]

@@brittonporter5063 yes

[@sheikhk.s.sarian2594]

"Y'all already didn't know that?" - This comment was made by Asian Gang

[@u.v.s.5583]

It is also standard, I believe, in most of Eastern Europe.

[@kartik5876]

This was so basic... I didn't know this method had a name. We were taught this before quadratic formula.

[@bhabeshkumar8804]

Being an asian indian I didn't know this method, although I know some different easy methods to solve this equation. Always happy to learn more.🥰

[@elonmusk2157]

Meet any CAT or CGL aspirent of india

[@AnuarLife]

I m from Russia and we use this formula and name of this “ the theorem of Viet” (Теорема Виета)😂😂😂

[@priyankaaggarwal1982]

Everyone gangsta here untill complex roots enters 😂

[@souls5180]

Oh no guess I have to change my name now 😅

[@souls5180]

@@MKD1101 pehle mera naam Gangster Sharma tha then i changed it .

[@souls5180]

@@MKD1101 please bhai , yeh mat karo .. ruk jao .

[@anitakajala7799]

Please don't comment without having a prior knowledge of complex no.s

[@priyankaaggarwal1982]

@@anitakajala7799 Expert in it bro mind your own work 😏

[@theTHwa3tes11]

Math Teacher: You weren't supposed to do that!

[@lxna5889]

Grrrrr

[@gabrielasr9744]

This guy just seems so happy teaching ❤️ This can really change a lecture for the better

[@sonalikakade3484]

Dude, we learnt this method in school!!

[@whatdoiputhere5089]

Wahi lmao

[@blueb0y980]

Indians are faster than this 😅

[@blueb0y980]

@shubh Yes, You are right he is better than that of tiktok jokers

[@avishek438]

He is not “dude”.. learn some manners..

[@bait5257]

@@avishek438 that's true too. Dude is little disrespecting

[@augf6354]

I've never seen a man this excited over teaching, congrats :D

[@GeoffCanyon]

Pretty sure this *is* the quadratic formula, just with a factored out.

[@BrightBlueJim]

That is correct. In fact, he SAYS that if a isn't 1, you have to factor it out first. If you factor a quadratic using this method, and then using the quadratic formula, you find yourself doing all the same arithmetic. The difference is that if you are good at remembering sequences of operations, this will seem easier, while if you are better at remembering formulas, the quadratic formula will seem easier. They all break down to different rearrangements of the prototypical quadratic, ax^2 + bx + c = 0, to solve for x.

[@valentinidk6101]

Lmao yea it is

[@Austin1990]

To be fair, it will all be algebraically equivalent no matter what you do. This is just a different way of thinking about it. The equation becomes: for a=1, x=(-b)/2 ± √[ (b/2)^2 - c ] Honestly, this would be an easier way of evaluating the quantity underneath the root if b is divisible by 2. But, most importantly, it gives a better conceptual understanding which can save you if you forget the quadratic equation.

[@dr.weirdbeard6054]

Thought so too!

[@ricardofraser4243]

when we complete the square its the same... the turning point -b/2a x-coordinate is the midpoint of the root ... the rest follows

[@gbeziuk]

It's Vieta formula's extension. They taught it in schools in USSR.

[@francescopiccolo2000]

Minchia in Russia siete fortissimi

[@shorge37]

In russia too

[@infinixgaming1791]

well in india too.. we are taught vieta formula.. x^2 - (sum of roots) x + (product of roots)

[@heyman9078]

@@infinixgaming1791 it's a bit different. i learned that 3 years ago, but the loh's method use de discriminant for quadratic equations in a ''indirect'' form the ∆=b^2-4ac is equal to u. since there are many equations that cannot use x^2-sum+product.

[@imnotarobot6927]

Following along with this made me realize where the rule "If a polynomial has integer roots, they evenly divide the constant term of the polynomial" comes from because if you expand (x - x1)(x - x2)(x - x3)... the last/constant term will always be x1*x2*x3*... I was always just told, "if you want to guess integer roots, guess all the factors of the constant term" and never questioned it. yay, learning

[@BrightBlueJim]

Yeah. This lets you guess the roots when they are integers. Which is fine for passing math tests, but doesn't come up so much in the real world.

[@davidseed2939]

i was taught almost this method in 1965. rearrange the original equation as x² +2hx +d. then x= -h +/-√(h² - d)

[@BrightBlueJim]

This is correct, but I'd like to point out that you would get the quadratic equation once you're rearranged the original equation to factor out the x^2 coefficient. So you end up doing exactly the same arithmetic either way, but the method you are showing splits it into two steps. What makes the quadratic equation nice is that once you have it memorized, it's just one step. So really it's a matter of whether you want to remember one equation, or a slightly simpler equation and another step. What I like about the method shown in the video is that you don't have to memorize anything, and even if you forget the exact process, it takes only a minute to go through the same derivation the describes.

[@-ClerzZ-]

I'm pretty sure I was taught a formula as x^2 +2ab + b

[@BrightBlueJim]

@@-ClerzZ- I'm pretty sure you weren't, because that would not have given you the correct answers. In fact, it doesn't even solve for x.

[@sasoblazic]

I agree. This video really does not add anything new to the solution of the famous equation. But how could it? Everything here is completely known for centuries.

[@BrightBlueJim]

@@sasoblazic It gives students another option. The math is what it is. Whether you are plugging a, b, and c into the quadratic equation, or you're factoring by completing the square, or you're using this method, the actual arithmetic you are doing is identical. But different people remember things in different ways, so for someone who has no trouble remembering complicated equations, the quadratic equation may be the best way, while for people for whom remembering the steps in a process is easier, then this method or completing the square may be easier. You are right: this method that David Seed describes doesn't add anything to the mathematics, because just as what is described in the video is actually one derivation of the quadratic equation, and completing the squares is another, this is just preparing your polynomial a bit before crunching the coefficients through a simplified version of the quadratic equation. But for every student, ONE of these methods will click better in their mind. There are also cases, though, that are easier to do with one method than another. For example, if the x^2 coefficient is 1, David Seed's formula is slightly easier to use than the more general quadratic equation, and if your coefficients are all integers, completing the square or the method in the video may be easier to apply.

[@ayubjikani5401]

I can summarise, If u²>0, Eq. Has two real roots. u²=0, Eq. Has only one real root. u²

[@ceres8494]

Everyone:Using this method Me: nEgaTiVe Beeeeeeee pLus oR mInuS tHe SqUaRe rOoT oF....

[@ndakeren8673]

FFFFFFFFFFF

[@Fakipo]

It also tells you if the roots are real or not. For me its a lot quicker to solve using that formula. The only problem is remembering it by heart.

[@bonnieb7608]

Omg now I have that song stuck in my head again 🤦🤣

[@ceres8494]

@@Fakipo join the cult kzbin.info/www/bejne/e2PIh418rp6ssM0

[@ceres8494]

@@bonnieb7608 yes

[@karlstephenevallo6543]

Definitey I want a professor like him because he has that kind of amazing aura that relaxes the mind of students listening, he has that kind of smile that lets you chill with the process making it look easy and last thing is his voice its so mesmerizing that you may not know your subject relates to math. Last thing, the method you used is very easy to understand and way more beneficial to do irrational or the complex root without using that much of calculations. Thank you for discussing and here I am hitting that subscribe button and ringing that bell icon sir. God bless us all.

[@caurixportal1332]

But in real life, and nature, the coefficients could be ANYTHING, not so nice and simple. You need a repettive method that works fir ever single situation. Does this one do it.?

[@rubensramos6458]

For example, the solution of x^2.01-5x+6=0 is x = ((-5/1.01)Wq((-1.01/5)*((6/5)^1.01)))^(1/1.01) = 2.0302 (up to 4 digits). Wq(z) is the Lambert-Tsallis function and, for this case, the parameter q has the value q = 1-1/1.01.

[@jabunapg1387]

Everybody learns this formula in school in Germany. It's called Vieta's Formula or p-q-Formula (the general solution formula).

[@pizzamidhead2183]

also in Italy, it is considered the basis of second degree equations, you learn in the first grade

[@stepanosipenko5032]

Also in Russia, it is one of the basic formulas

[@cyto3338]

Never studied it as a part of curriculum in India

[@phantom_drone]

@@pizzamidhead2183 I knew Italians were smart, but how do you teach quadratics to 6 year olds. That’s crazy

[@alenvaneci]

@@phantom_drone Probably first-grade high school students.

[@matiassantacruz5487]

I love how he says “it’s a nightmare” 😂 5:18

[@lxna5889]

LMAO

[@srchillout4848]

-b+-√b²-4ac/2a : am I a nightmare 😤

[@chriswasabii]

WOOOOOWWW!! My highschool teacher taught me a slightly different variant of this method that was harder to understand back then. This video is very clear, very useful and well done. Great job!

[@i_am_me1238]

I'm not gonna lie, his accent made me watch the the whole video! 😐

[@september1683]

Oh, he really has an accent? I didn't notice that! :-)

[@hridoysarkar050]

Legend: Uses the quadratic formula. Ultra Legend: Uses this method. Me: I use my calculator.

[@amitavadass]

West Bengal naki Bangladesh???? INDIA te to calculator allow kore na wbjee &jee main etc te!

[@DANTE-kv7mv]

@@amitavadass maybe he's in a college

[@amitavadass]

@@DANTE-kv7mv hoyto!

[@labib1782]

@@amitavadass Bangladesh eo korena dada

[@sumonsohailbnc2059]

@@amitavadass jee 2021 or 2022

[@asal2667]

Bro this is literally what's taught in Asian schools. I never thought this formula would change my life lol

[@hamzamoussaid8895]

american educatio system bro i studied this in 7th grade morocco btw

[@asal2667]

@@hamzamoussaid8895 yep american system too boring, long and dumb

[@dmitricherleto8234]

@@asal2667 bro, then why almost every best university in the world is in U.S?????

[@christiancabrera8926]

@@dmitricherleto8234 university and college maybe...but K-12 hell no

[@asal2667]

@@dmitricherleto8234 on what basis do you call it the best? just because they say so?

[@colinbrash]

This is cool, I’d never seen it before. Another way to think about it: you convert the polynomial to the form x^2 - 2bx + c, and then the quadratic formula reduces to just b +/- sqrt(b^2 - c)

[@GG4EVA623]

Wait so do I use the one you suggested? Instead of quadratic equation

[@interiorcrocodile4297]

@@GG4EVA623 not always valid

[@paradoxicallyexcellent5138]

This is my preferred method when doing physics and dealing with a bunch of physical constants. I find it quite clean.

[@sillasaram9121]

@@interiorcrocodile4297 When is it not valid? It is valid for all cases since new definition of "b" is now 1/2 of old b.

[@theengineeringstudent2678]

If everyone spoke English as you do, life would be better.

[@m.a.y.u.k.h]

Correct

[@DouglasHPlumb]

I like his enthusiasm, he is very good at this, but Yikes.

[@Manu-Alpha]

Yes

[@ervivekchoubey]

x²-2x+8/9=0 -> 9x²-18x+8=0 Product of coefficients of x² and the constant=9*8=72=12*6 (because 12+6=18 which is the sum of roots). But sum is -ve coefficient in the equation so we take (-12)* (-6) Now just divide these two factors by the coefficient of x² and change the sign. i.e, 12/9 and 6/9 = 4/3 and 2/3 which is the answer.

[@pawansoni-sg6he]

Sri dhracharya rule to find roots of quadratic equation is way better and easy...

[@mathsacademy2652]

Yes Sridhar Acharya's method is more easier.

[@saumyamaurya2603]

Yes. They are fools😅

[@pawansoni-sg6he]

@ayo tebak siapa and why u feeling jealous by this? This is true...evan u also use this method

[@mimzim7141]

Give 20 second degree equations with random coefficients to a person and let him solve 10 with usual quadratic and 10 with this method and see which is faster.

[@hungryplate400]

@Left and Right Troll For a Computer, the quadratic formula is better, because, it doesn't have to "think", rather input values in a pre defined formula

[@Tyns19]

work the method shown in the video symbolically and you will find that it reduces to the usual quadratic formula. The method shown is only another way to derive the conventional quadratic formula that we are all familiar with. just start with: x^2+bx+c=0, and follow steps in the video.

[@adrien8572]

@Left and Right Troll Yeah like when i was in high school we had the right to use a calculator and we had a program calculating the solutions instantly...

[@mimzim7141]

i understand it is equivalent to the usual formula. And if you think of it has to be since it gives the correct solutions. Now i tried a few times and it is not as slow as i first thought, with some practice it could become a viable computational option. Another test to do is wether that method increases or decreases your percentage of calculation mistakes.

[@rayray6548]

@@adrien8572 so your calculator got the school degree, not you. son..

[@BlankTH]

This is essentially completing the square since it's all the same operations. Using the first example of x^2-6x+8, finding the midpoint is creating the square (x-3)^2, then the operation where he finds the distance is just moving the 8 over and adding the 9 from the square giving us (x-3)^2=9-8=1, then square root both sides and move the 3 over, 3+-1=2 and 4. It's exactly the same method. But then again, so is the quadratic formula, as it's derived from completing the square. It's all the same. That being said, the value of this video lies in the geometric intuation it gives us for completing the square. I never had that before, it was always just something that I could kind of sense in the background while completing the square. Having geometric intuition for the maths you do helps you understand how everything flows in a deeper way, and that's what makes this video good.

[@MiroslawHorbal]

Only took me 32 years of my life to stop using the quadratic formula. TY. I know what I'll be teaching my kids when they are studying quadratics in school!

[@chocolateangel8743]

If they're more visual math learners, like me, they might prefer to Complete The Square, using an area model (the same thing).

[@d6853]

No, don’t do that. They are taught the formula for a reason, most questions will require the formula, you get marks for working, if you do that you will confuse them and they will lose marks

[@arunkumarcs9191]

I thank KZbin algorithm for showing me this videos in my recommendation. And thank you sir.

[@wannadieirl6155]

Lmaooo

[@H336-p1v]

in russia, Vieta's theorem is taught in grade 8, so I don't understand your delight :D P.s. srr for bad eng, its google translate :3

[@gvarun0403]

He's from West

[@hanzhoutang9235]

In China, the method was taught in grade 7... But it’s a great method, anyway.

[@andrewmathematician7443]

Here in Czechia, it's taught in 6 grade, maybe even in kindergarten we spoke about it among boys... (Just joking, I am not from Czechia)

[@navedhasan9722]

@@hanzhoutang9235 Chinese people are machines! They work alot to use their full potential. I am a 10 grader and learnt it for the very first time

[@imposteristixx6877]

The way he talks and moves is adorable

[@AAAAAA-gj2di]

and the way he derives and then uses the discriminant formula in every quadratic equation

[@Majestic469]

@@AAAAAA-gj2di lol

[@rajakumari3716]

@@deelakayahaladeniya4472 ur gay

[@gibbogle]

Not to me.

[@miak5929]

Its hay

[@goofygoober6211]

im in Calculus BC in my senior year of high school in the United States and I've never been taught this!! so cool

[@TheOldGuy2000]

It's just a parameter change. What you show here is that using this approach for this particular quad equation that you can solve for real roots perhaps as fast or a little faster. Point 1: The amount of work is no longer or shorter in general compared to traditional quad formula. This depends on your equation. Point 2:With this method you lose the intuitive nature of the Quad Formula. At a glance a person who has learned Quad formula can get the center info exactly the same as one does with this method. The rest of quad formula is just the distance on either side of this center. Where the quad formula is better though is that one can tell at a glance if the relationship has real or complex roots and finally how many of each. Try this equation, 10x^2 +2x+1= 0 and race someone who uses quad formula to answer. First tell me, will you have one real, two real, or complex roots before you calculate the center (use only the knowledge of your method). A quad formula user can do this in seconds. Anyone can write a quad equation in such a way that it slightly benefits one method of calculation over another. That does not mean that some method using an arbitrary parameter change is necessarily a better method overall. I am sure someone could show you a different parameter change then cherry pick a good quad equation to solve quickly with it. IMO, this method falls far short of the value of quad formula since you lose all intuitive info indirectly supplied by quad formula. When we teach, we should first gain a deep understanding of our material. I don't think this method is anything new. I believe it was how the ancient Sumerians and then Babylonians solved in a similar fashion.

[@ajaysane3426]

We have learned much much easier method insolving these equations in India. Now our pride in our education system increased manifold after viewing this video.

[@srijanbhowmick9570]

Seems sus why Dr . Peyam didn't heart ur comment altough he hearts everyone's comments

[@muffin_____]

Me looking at the title, "I bet this has something to do with viete's theorem" sure enough it does! Just learned about this in class this semester

[@janvisagie231]

I like the fact that you explicitly wrote the implicit explanation for why Po-Shen Loh's method (yeah I just watched his vid beforehand) works. However I have one question, shouldn't this equation be equally valid if you use (x+x1)(X+x2) instead of (x-x1)(X-x2)...that way you won't have to keep changing the sign of the second term in the original equation e.g. in the equation at 2:08 the midpoint will be -3 instead of 3. I know you will have to change the sign of x1 and x2 to eventually get the roots though when using the form (x+x1)(X+x2), which is likely why you are using the form (x-x1)(X-x2).

[@coldlogiccrusader365]

TY, I cam to the same conclusion how can the sum of the roots be < 0 yet they are both positive.

[@mayaghazy391]

Love the fact that this got recommended to me when I’m about to have my exam in 2 weeks 😀

[@wp2kkopyyuu78]

I too.

[@martinj.montag.amritapuri8208]

Careful, in exams it can be equally important that you're examiner recognises you go a "working" way to the solution. Then, if you make a mistake they may give you marks for the way to the solution. (Still, I agree it's a wonderful way, especially because it always goes with understanding of how the solution works.)

[@KayOScode]

How did it go?

[@mayaghazy391]

@@KayOScode it was extremely easy actually

[@KayOScode]

@@mayaghazy391 I love it when theyre easy. Hoping my compilers midterm is easy this Wednesday lol

[@Maddof_Erroz]

"Change my life" is a bit far of a sketch but, still interesting. I never thought that there might be different ways to do maths. Learning maths like a religion seems wrong. Learning anything like a religion seems wrong. This sparked my curiousity to find simpler ways to solve problems, rather than following the herd. Ofcourse understanding the fundamentals is necessary, but sometimes teachers make things so complicated for no reason. Nevertheless, this was helpful in a way and therefore, I am grateful.

[@yugandhar9247]

2:40 just put x1 = 8/x2 in upper equation you will directly get the answer

[@alakas706]

This is just the quadratic formula done as an algorithm. Very nice

[@Metalhammer1993]

yup more exactly the variation of the quadratic used in Germany and India. The Pq-formula. (way less of a headache than the American formula and all you really do is divide by a)

[@alakas706]

@@Metalhammer1993 Yeah, can belive so. remaber when I first learned the formula, was a headice to memorice

[@Metalhammer1993]

@@alakas706 the american one really is a monster. the PQ one is a bit simpler

[@m.m.2341]

My God, the rest of the world uses the ABC formula? I hate that monster.

[@Metalhammer1993]

@@m.m.2341 yup. I at least only know Germany and India

[@Icenri]

It's so smart! Why is it not taught everywhere?!

[@fullfungo]

Because it actually IS taught. It is based on completing the square, which is a method used in deriving the standard quadratic formula. If you recall its derivation, you can clearly see how they are identical.

[@Icenri]

@@fullfungo Yes, I know that this is how the Greeks worked it out as well, but schools just sit down you in front of the equation.

[@leif1075]

@@fullfungo then why is he touting it's different if it's the same?

[@KaiHenningsen]

@@Icenri They do? I don't recall that ever happening for me. Maybe it's just some places where it's taught worse?

[@fullfungo]

@@leif1075 Having different methods to obtain the same result may seem pointless. However, some of them may be more intuitive for a human, while others are more efficient for a computer. There are of course other reasons, but these two are usually the ones that help us make the choice when presented with one.

[@hansduran9462]

I independently discovered it myself, too, when I was in highschool! I call it "The MD Method". It has three steps: 1. M= -b/2a 2. D= (M²-c/a)^½ 3. x= M±D Hope this helps. After some more scribbling, I found out that it's basically just quadratic equation torn apart. LOL.

[@Handelsbilanzdefizit]

>>>The Quadratic Formula that will change your life

[@chocolateangel8743]

🤣

[@anandjha7311]

😂

[@SuperRiddhish]

Than change your wife

[@bharat_bhattacharya]

Epic🤣🤣🤣🤣🤣

[@muhammadarham7442]

I like his voice: magical. Imagine a kid has difficulties in his or her life. The kid enters a lab and meets a nice wizard. You are the one. Thank you and just subscribed to your channel. I think next time you should assemble a set where it shows magical world. You are the wizard mathematician. Your channel will go to the root.... sorry I mean go to the roof.

[@theproofessayist8441]

It's very interesting how this method that Professor Po Shen Loh has popularized in his framework is midpoint centric whereas the completing the square method to get the quadratic formula is very area centric. The 2nd paradigm hails back all the way from Al Khwarizmi's time as you say - I'll take your word midpoint paradigm existed since ancient Babylon as well it's just its going through a weird resurgence in popularity, 1st back when it was conceived, 2nd when Francois Viete and other French mathematicians looked at sum and product of roots of polynomials, and now today with Po Shen Loh and you Dr Peyam.

[@dramwertz4833]

The pq-formel one learns in germany is basically the same just put into one formula. Always am perplexed that quadratic formula is used in america

[@Ocklepod]

it's too hard to teach students to divide by leading coefficient.

[@eskybakzu712]

I would assume that it is because the pq-formula is the solution to the equation x^2 + px + q = 0, while the quadratic formula instead solves ax^2 + bx + c = 0, meaning that, it is originally intuitively easier to understand the application of the quadratic formula, since it practically works for all quadratic equations, while the pq-formula occasionally requires simplification of the equation to fit the standard form.

[@GaussianEntity]

Teaching US students a simplified method would lead to a LOT of confusion when dealing with more complex quadratic equations. I've seen a lot of different methods taught by teachers and the confusion isn't diminished among students, so I don't think it's the method that's the problem.

[@nathanisbored]

@@GaussianEntity if anything its the number of different methods that confuses students

[@musik350]

People in this country are actually presented with either of both formulae.

[@elmanu3114]

This method is practical as long as a=1 and b is even. And in that case you can use an even more practical method which comes from dividing both the numerator and denominator by 2: Let β=b/2, then x=(-b±√(b²-4ac))/2a=(-β±√(β²-ac))/a And if a=1, then x=-β±√(β²-c)

[@danimantovani26]

b can be odd, you would just need to work with a fraction, and you can always divide an equation by a so that a=1

[@devankitshukla1370]

This method is derived from Sridhar Acharya formula sum of roots -b/a and product of root is c/a in quadratic ax²+bx+c

[@drpeyam]

It’s the other way around, your formula follows from this method

[@Numidium_]

I didn’t click for this. I just lost my last brain cell.

[@curiouscase]

I am an Indian...that too from Bihar which is traditionally known for Its Mathematical acumen and guess what , this method was taught to us in 10th grade.😎

[@diwas4696]

guess what I am from Nepal and this method was taught to us in 9th grade

[@ScalpeL02]

@@diwas4696 destroyed in seconds ! Well that's not true though.

[@lolubom6721]

Ya bro I am in class 9th and I know this, but I use different trick

[@mannudevsah5326]

This method taught to us in 6th grade

[@lolubom6721]

@@mannudevsah5326 😂 kar diya chutiyapa😂😂 bhai 6 grade me kisne padha polynomials, factorization and all that 😂

[@AyushJoshi-y8c]

Not gonna lie our teacher taught this first in middle school before quadratic formula, Indian maths teacher rocks

[@edwincuevas9965]

Engineers: "just type it into Matlab!"

[@rudrasama297]

@Fahad Zafar its language to represent to Visualise data

[@robinsingh9102]

@@rudrasama297 "to represent to visualise data" Godzilla had a heart attack reading this

[@rudrasama297]

@@robinsingh9102 is he Dead now? Or you transplanted your heart?

[@carterwoodson8818]

This is basically depressing a polynomial no? This is related to an important step in solving the general cubic equation.

[@easymathematik]

Yes it is.

[@LKRaider]

That’s harsh, we should be nice to the polynomial to help it overcome its depressive roots

[@easymathematik]

Depressing a quadratic is equivalent to "completing the square".

[@faysal...]

1 year on and Dr.Peyam is still giving hearts

[@pedrocaetano3366]

i wish my math teachers were as cheerful as he, i would have learn math.

[@dragster9474]

I think your English teacher was also not cheerful

[@dragster9474]

😂

[@hardikjindal7010]

@@dragster9474 🤣🤣

[@hardikjindal7010]

@Aadi Ringay which method?

[@prafulyadav2658]

I'm pretty sure u would be making fun of him

[@shrutigupta250]

So are you saying that people didn't know this? Like before learning the quadratic formula?

[@sarbjeetsingh9137]

Yes.. in NCERT its done before doing quadratic formula.😂in 10th

[@lime-limelight]

@@sarbjeetsingh9137 I know but nobody uses, all do these questions with the splitting the middle term Tho these identities were told in class 9

[@sumantakumarrout2432]

@@lime-limelight that's true what you said tanish

[@IITians]

Just apply Shri Dharacharya's quadratic formula 😄 it'll save your time.

[@jitendragautam1865]

don't think western guys are that good at maths ...i saw another video where goras were surprised seeing Indians telling squares and square roots of natural numbers .

[@rubensramos6458]

On the other hand, the general analytical solution of a^x + b^x = c^x can be found in "On the Solutions of a^x + b^x = c^x" that can be download on Researchgate too.

[@vasilisgrekas4225]

They have literally told us in school but now I understand where it comes from

[@akshatporwaliitmadras1438]

Huh! This kind of methords are everyday used in class 11 problems for IIT JEE

[@vishalkhod6280]

Proud to be jee aspirant 😊

[@arjakroy8433]

Yes🤣.. in india 10th ka bachha ye kr lega😆

[@komalsinghx]

Mein to ye 6 class mein sikh liya tha 😂😂

[@Khan_Ustad]

My life changed after watching this video, now I drive a lambo and live in a castle. Thanx dude.

[@MrRyanroberson1]

the reason it was 'tarnished' with the quadratic formula: look at the quadratic formula with a=1. x = -b/2 ± sqrt( (b/2)^2 - c); this is exactly the formula you presented: the midpoint is -b/2, and from this midpoint m, you get (m-u)(m+u) = m^2-u^2 = c, then u = sqrt(m^2-c), and x = m±u, hence -b/2 ± sqrt( (b/2)^2 - c)

[@bevvy.bee9]

Ah yes, I lost track while reading but this seems right

[@tobeymaguire647]

Yup agree 👁️👄👁️

[@nasirfshah]

Oh dear , thought I will learn some new method. Have already covered this in my elementary mathematics class back in school when I was a 6th grader. Anyways , Kudos to your enthusiasm 🎉

[@anshikagupta1114]

You are from which country?

[@jyo5464]

Same here

[@akshatj4546]

@@anshikagupta1114 India me bhi 6 class me krate h यह kha se aagyi tu?

[@anshikagupta1114]

@@akshatj4546 I am also from India but I learnt this in 9th standard

[@ming2k]

Back in 1980s when I was in junior high, one of my math teachers in China taught us below formula to solve any quadratic equations ax^2 + bx + c = 0, then we have (-b/(2a) - u)(-b/(2a) + u) = c/a, then we have (u + b/(2a))(u - b/(2a)) = -c/a. Solve the u we will get x = -b/(2a) - u or x = -b/(2a) + u.

[@martin-__-]

this generalizes into the quadratic formula

[@FrankTuesday]

I was curious, so I did the work using A,B and C for the coefficients and was not surprised that they quadratic came out. I guess some people do better memorizing a formula, and others do better memorizing a method. I'll stick to the quadratic.

[@cgaran9943]

@@FrankTuesday And madmen compute the quadratic formula from the general form of the quadratic equation in the middle of the test.

[@bobross5716]

yes but this can be used for higher order polynomials

[@martin-__-]

@@bobross5716 how?

[@bobross5716]

@@martin-__- just add more terms when you initially factor out the equation e.g. (x-x1)(x-x2)(x-x3)... and continue the process from there.

[@easymathematik]

This is more or less an algorithmic way of the pq-formula.

[@tobibender7475]

And pq is even more simple and easier to use

[@easymathematik]

@@tobibender7475 The point is not about "more simple and easier". It is about following: An algorithm does not explain why it works. It is just: Make step 1, step 2, step 3, ... the pq-formula or abc-formula or what ever explains, why it works. This is the difference.

[@hjs6102]

@@easymathematik In school, we learned how to get from x²+px+q=0 to the pq-Formel. Afterwards, we used it to calculate fast.

[@Therealhamidreza]

For finding midpoint you can say In ax^2+bx+c = 0 The midpoint is - b/2a & for product It's c/a It works absolutely You can even draw this equation easily

[@7rgrov198]

I always thought of it like: how can i factor the last coefficient and sum/subtract those terms together to make the second coefficient.

[@BrightBlueJim]

That was how they taught us to factor quadratics first, but I kept asking, "but what if the factors aren't nice, round numbers", to which I was told, "don't worry, we'll get to that", and that turned out to be the quadratic equation, which always works. I think they only made us learn to figure out pairs that multiplied to b and added to c, was so that we would learn to recognize the easy cases, and avoid using the full formula.

[@BrightBlueJim]

That was how they taught us to factor quadratics first, but I kept asking, "but what if the factors aren't nice, round numbers", to which I was told, "don't worry, we'll get to that", and that turned out to be the quadratic equation, which always works. I think they only made us learn to figure out pairs that multiplied to b and added to c, was so that we would learn to recognize the easy cases, and avoid using the full formula.

[@7rgrov198]

@@BrightBlueJim sure, but for almost all cases that you are likely to encounter, the coefficients arent fractions

[@BrightBlueJim]

@@7rgrov198 That may be the case when you're taking an algebra test in high school, but when you are solving for the poles in an electrical circuit, the coefficients come from some combination of multiple electric component values, the coefiicients are almost never integers. This is just one example. Every place I've seen where I've actually had to solve a real world problem (as opposed to a problem in a textbook), I've had non-integer coefficients to deal with. I've come to realize that it's far easier to just plug the numbers into the quadratic formula, than to use one of these "shortcuts".

[@chongweifongchongweifong7180]

the general quadratic equation is ax^2+bx+c=0, and of course, you can divide both sides by a and get x^2+b'x+c'=0, where b'=b/a and c'=c/a. If you work like dr peyam, the formula you will get is x=m + or - √(m^2+c') where m=-b'/2. But if you substitute everything back in, you will just get the original quadratic formula. So maybe you can say its a simplified version, but not a new method?

[@cjmq1970]

I’m a half century, first time in my freaking life I see this method, I was always taught to “use your instincts’ basically instead of the midpoint and the minus sign before the second term of the equation. Well, I thunk that after 25 years of obtaining my university degree, my certified professional title and 27 years of labor experience (yes, I started working on my career two years prior to license and degree), it’s never too late to learn something.

[@t.n.t1229]

Change variables, this technique is usually used to simplify Cubic and Quartic equation but it's so strong with Quadratic equation, we had Delta and Vieta fomulas. Anyway, this method is nice :))

[@mrmexicano64]

I find The logic to be pretty similar to Mohr's circle

[@sssilky3317]

I just started my new job as a math tutor and I'm going to try using this to help my students better understand quadratics, Thank you Dr. Peyam

[@drpeyam]

Awesome!!!

[@rishabhasthana1936]

Thank you sir! Very insightful, makes me want to play with maths with a different perspective....wow truly eye opening

[@samonterolanjayp.8229]

I thought we just have to find pair of factors of the c, and if that pair's sum is the value of the b, then those are roots (in ax²+bx+c). Isn't this simplified factor method easier than the video? We can even calculate using this mentally on our 7th

[@drpeyam]

In general if the roots are irrational, then no

[@brucesing2089]

Rolan Samonte this kind of vidoes could save you much time looking for the correct answers

[@fuiijutsushikifuujin9413]

For irrational roots, it's hard, it may take time.. It's possible but it ain't easy.

[@WontTrout]

Great video! Worth mentioning that this is really just the quadratic formula, from an understanding perspective rather than a "plug and play" perspective.

[@isi2973]

That honestly reminds me alot of the p-q-Formular wivh is a simplified version of the quadratic formula.

[@garyhuntress6871]

Am I the only one that thinks the mid-point diagrams with the two "U"s over them look like cats?

[@nullplan01]

Now I can't unsee it.

[@felipevasconcelos6736]

UwU

[@vanessakitty8867]

Good catch. Yes they do.

[@BrightBlueJim]

No, but that, combined with the two 'U's over it led me to wonder if it was going to end up being a drawing of a dog's face, or something.

[@DeanCalhoun]

this way can be written as x=m+-sqrt(m^2-d) where m is the midpoint for the normalized equation and d is the constant term of the normalized equation. we can easily achieve the quadratic formula from this: we have ax^2+bx+c and then we normalize to get the scaled equation x^2+(b/a)x+c/a which has the same roots here we see m=-b/2a and d=c/a plugging in these values into the formula above will give you the quadratic formula after some simplification

[@harrygraham9690]

Everyone learns this if you do A level further maths, it’s a topic called roots of polynomials

[@Stxrmz]

Ah yes, a fellow further mathematician

[@harrygraham9690]

@@Stxrmz well hello there. AQA?

[@Stxrmz]

@@harrygraham9690 Edexcel

[@akhilkumar3090]

I read it during JEE prep

[@TanishqTulsi]

Wait I know that I call it my jugadu formula. Came up with it during my maths test. ❤️

[@yousubtube]

Very few will understand this new english word 'jugadu'.However it's good.

[@carmelpule8493]

Dr Peyam is a wonderful gentleman teacher. This should have been explained stating why it works . I shall explain . if a quadratic A*x^2 + B*X +C = 0 then if we plot y= A*x^2 + B*X +C we find that this is a summation of three individual functions as (A*x^2) ( parabola) + added to ( B*X)( straight line) and added to (C ) a shifting constant. If they are plotted individually then we have A will open and close the parabola X^2 B will shift the parabola to the left or the right and even up and down keeping the parabola A*X^2 in the same orientation. C will short the parabola A^X^2 up and down on the Y axis keeping its shape and its orientation. It is because the curve keeps its orientation and its symmetry that this method works. Knowing this then as detectives we need to look for the minimum location of this function hence we need to differential the function and equate it to zero. y= A*x^2 + B*X +C let us put it in the form of y = X^2 +K1*X + K2 K1 = sum of roots and K2= product of roots y = X^2 +K1*X + K2 it is convenient to take all constants as being positive. dy/dx= for minimum = 0= 2*X + K1 hence Y is a minimum at X= --(K1)/2 NOTE THE NEGATIVE SIGN ATTACHED TO IT. Then proceed taking into account the negative sign. of where the minimum is located. It is because of this symmetry that the average of the roots is located in the middle! Let us solve for ( X+4)*(X+2) =0= X^2 + (2+4)*x + 4*2 =0 Note the negative sign hence average of roots is (--6/2) hence ( --6/2 +U)*( --6/2 +U)= 4*2 = 8 hence (6/2)^2 -U^2= 8 9 --U^2=8 1 = U^2 hence U= + or - 1 and this in conjunction with the mid location of roots root = -3+1= --2 and other root is --3-1 = --4 which is the solution of equation ( X+4)*(X+2) =0 The reason this works because the coefficients do not alter the orientation nor the symmetry of the curve hence he MINIMUM POiNT of the curve is always in the centre of the two roots. I prefer to consider all the coefficient as being positive and the differentiation that follows to find the minimum point follows automatically to produce the negative sign, in the mean of the roots, I rather do that than introduce the two negatives Dr Peyam used when he had a positive coefficient, This also works when the roots are in vector form which can be interpreted as the solution having a rotation!

[@pedramkeshavarz6212]

It is in Iran's education system and we are taught in h_school this kinda stuff for our big test called "konkor".