Algebra 2 - Roots and Zeros, Descartes Rule of Signs

Renee Descartes gave us some cool stuff. "I think, therefore I am." Whoa, deep. But what's also deep is his discovery about the sign changes in a polynomial. Using his Rule of Signs, we can uncover how many positive zeros, negative zeros, and imaginary zeros exist for any polynomial. Merci beaucoup, Monsieur Descartes, et YAY MATH!
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[@oliviagoodroad8339]

Every math teacher should be required to watch this guy in training so they know what good teaching looks like.

[@asphyxiuh]

@@mirajones1295 that escalated quickly

[@mhorton7217]

This is my first year teaching Algebra 2, so that is exactly why I am watching this video.

[@Orion-gw7kg]

I have committed several war crimes in Syria and currently am holding multiple captives hostage in a hospital in Idilib.

[@Gorgun2010]

This guy deserves a gold medal for how good he teaches.

[@kerrymcq9208]

I wish every class was this cooperative! In 20 minutes of my class, I would have 42 interruptions and everyone would leave confused.

[@ungdung_i]

thank godddd for this video, my precalc teacher can't teach anything

[@oneilstewart9381]

True

[@josephchadwickromulo8731]

i thought i am the only one that has a teacher who cant teach hahahahaah

[@oversteer1000]

Many thanks for the detailed explanation. I am self teaching myself college level algebra and the book's explanation of Descartes Rule of Signs was a total confusing mess. Again thanks again.

[@danichi5918]

Even after 4 years this is still the best explanation of this lesson I've seen on KZbin

[@sohamdutta9281]

You still have not watched Indian education you toube channels. They are the best on you toube, with most number of subscribers

[@noelebmafay9132]

The best video !!! Great professor !!! The reactions of the students are funny, and it's always like that. Now I mastered the Descartes's rule of signs.

[@APham-bd2ih]

I wish you were my teacher. My algebra teacher was supposed to be a sub, but we couldn't find a new teacher. and she only taught preschool ebfore

[@b33clipz39]

You're my hero I was failing algebra II

[@chillie2552]

Love this video. The only suggestion I would make is to have your students use the rational root theorem to decide which positive integers should be checked.

[@lilaznkeo]

Great Video!! Omg, this was what I needed!! Thank You!!

[@daveytandtheplacetobe7561]

your students sound like a real joy to teach; if only we could see them, too!

[@AshLonewolf]

Very helpful! Always watch this guy when doing homework I don't understand.

[@ELLYG.Benjamin]

can we use our imaginary number to solve in synthetic division. And also if we slot in the positive possibilities in the polynomials are the answers going to be zero.

[@yaymath]

Yes, to both your questions. Imaginaries are possible in synthetic division. And yes, the remainder will be zero for any candidate solution.

[@elyriaskateboarding4414]

Yay Math for president

[@JoshuaPenaranda]

Yo thanks so much, i missed 2 days of math class because of a school competition and this video really helped me catch up.

[@toridezvarriano100]

Thank you so much for this!! Explained so well and I actually understood it versus me trying to catch it when my teacher tried to. By far the most helpful!

[@denvercharlebois699]

You could just do factor theorem be way easier. Find that the pairing for the last leading coefficient and then find that 2 equals 0 which becomes (x-2) then do long division to find the other roots.

[@jenni.ayala27]

How did you get the imaginary numbers? confuse on how you got 0,2,4

[@shahin2324]

I'm cramming for my Calc exam tomorrow! :( Nice video btw!!!

[@samiesaid3618]

please make a video of appreciation and depreciation , o really need it so much +yay math

[@smellydonut5088]

thanks! i was so confused till now! :)

[@ranushree7680]

Thanks for Ur explanation sir is made me to go through descarts sign thank u very much sir

[@phillcarey4156]

The reason that the first two columns must be decreased by 2 is because there must be an even number of imaginary solutions if they do exist. That is, if 2i is a solution, then -2i must be a solution or if 1+i is a solution, then 1-i must be a solution.

[@robertojorgez6572]

Dope, you just explained it way better than my teacher, lol thanks bro....idk why people dont make it this easy like damn...i pay for them to teach me..

[@luiavalos92]

Great job in explaining the material!

[@ronaldomonteiro1031]

very well explained

[@noelebmafay9132]

yes

[@benadel1787]

but how did you know number to divide when using synthetic division

[@Gorgun2010]

the constant number in every term is used for synthetic division

[@sanisahara]

perfect explanation, thank you!!

[@deborahachimugu1783]

you, my man, are a savior

[@jaredpyke8073]

Didn't know Klay Thompson was a part time Math teacher 😂😂

[@ohseth7898]

Which one is the root? Is it the answer in synthetic division?

[@blessingzidyarukwa]

THANK YOU SIR

[@josesantossaavedra2834]

Thanks buddy, you save My life

[@IvonneGiles]

Yaymath is awesome!!!

[@MeridaRopertilovesyou]

thank you so much for making this video it helped me so much!!!

[@satyambhardwaj2289]

Merida Roperti Well I can teach you better than him!!

[@GeetaNakar]

Great professor!

[@sonofjesus1464]

Algebra 2 was very easy but that is because I love math. I will be taking precalculus and I heard it has a lot of trig. I did do some trig in the end of my algebra 2 course and it was very hard until I understood it. Then it became kind of easy but I still need to wrap my head around it haha :D

[@MK-kq2mi]

I love the new look with the Afro, I almost didn't recognize him ....

[@hachisu5288]

I'm 15 and trust me in our book this is our first lesson. For 3rd year of highschool. So thanks for the explanation.

[@noelebmafay9132]

what is your country?

[@simplechannel2909]

I would like to know how you get the five images the 4 you place on the image column like the image number

[@nesshingakusei6932]

Wait, which grade is this? We never studied this in grade school!

[@aleksandararabadzhiev3742]

Wonderfull content, major thumbs up.

[@diyamahajan8459]

Thank you so much!

[@ayushtiwari6815]

From.where country he is?

[@zaidahmad9927]

Thank uhh sir for this vedeo you are the best teacher

[@Day-et3fm]

This video saved me! But also tag yourself I'm the kids you can hear in the distance screaming

[@ronniegtv2827]

Once you get x squared -2x +2. Can’t you equal it to zero and use the quadratic formula?

[@AshLonewolf]

yes.

[@jenni.ayala27]

wish you were my math teacher!

[@mangaldanavhieversacademyi9709]

Wow! thank you so much Sir for the very nice and clear discussion explanation.

[@304neighborhood3]

0:15 what's the name

[@joannag1470]

God, thank you. I have a test tomorrow and had no idea how to do this.

[@satyambhardwaj2289]

Joanna G I can teach you..

[@liamthomas419]

thank you so much

This teacher is called “salvation”

[@stevensanchez8245]

I can feel the confusion coming from that room

[@matokin3189]

gracias estoy en medio de un exament y no lo sabia dios lo bendiga.

[@josephchadwickromulo8731]

i didnt know Klay Thompson is a Math teacher :0

[@hercaquino4750]

the comment I was searching for

[@Lele-xu5kn]

Damn, I don't even need that in my daily life

[@benadel1787]

but how did you know number to divide when using synthetic division

[@ayushtiwari6815]

Supposing whoes remainder is 0

[@jhoeannelim6018]

thank you

[@hridoydey8878]

thanks sir

[@بارقعمارفاضل]

what is the name of this topic and for which class?

[@Asmerom-Yohannes]

Bark200 Bk

[@priyanshubansal6776]

which class is this

[@rajivkumar-en9fv]

thnx sir ji

[@matthewrevoredo7591]

What is the noise at 4:34

[@emanabd9517]

Thanks

[@matthewrevoredo7591]

How do you know the number of imaginary solutions?

[@NitroticYT]

Yeah

[@NitroticYT]

I dont get it either

[@joeysusanoo5275]

im a little confused would a short cut be whatever the highest degree is than thats the number of possible for postive? Also i watched other videos the negative seems to always be zero is that always the case?

[@존레이-s3z]

How to get the imaginary number???

[@graciedavenport8572]

If Oscar Isaac became a math teacher

[@marthabfajardo1467]

can someone please explain to me how did he come up with a zero imaginary number? (5:44)

[@tntdragon1000]

I don't know if you figured this out yet, but since the total amount of possible zeros is 3, and there are 3 positive zeros, than that means there cannot be any imaginary zeros or negative zeros.

[@andreavisso7073]

Morty Yeah, but that's the possible amount of positive zeros, not negative zeros. Or do we always put zero for imaginary in the first row and then work from there?

[@sonofjesus1464]

I don't think he actually did that according to the curriculum. In Algebra 2, I never had that implied to the Descartes rule but maybe it's that way in Precalculus. I wouldn't worry about it too much unless you really want to know ahead of time :)

[@surrealist6726]

Andrea Visso Nasi the exponent of the leading x represents the number of possible roots. The number of sign changes represents the number of possible positive roots. The way to find the number of possible negative was explained. So basically the leftover number is what the imaginary number is. For example, if there were 5 possible roots and 2 were positive and 1 was negative then the leftover 2 is the number of possible imaginary roots. Though keep in mind that imaginary roots come in pairs so the number of imaginary roots can’t be an odd number.

[@hachisu5288]

Get the highest degree in the polynomial subtract it to the positive zero then subtract it to the negative zero.

[@deb6247]

How to solve 9n square-3n-8 =-10?

[@deb6247]

Discriminant of each quadratic equation then state the number of real and imaginary solutions

[@LiveGoodPhilippines888]

but why +7 didnt became a - ?

[@GeetaNakar]

👍

[@catherineferreira4518]

hi Mr .Robert

[@BigBlastP]

Does the teacher remind anyone of Ted Mosby from HIMYM

[@oscarwang7920]

just changed my major after watching this s

[@swastikamishra4759]

This was really good but nobody teaches in depth 😥😥 I'm waiting for in depth teachings

[@nesshingakusei6932]

That's what students should investigate themselves. You'll comprehend it much better that way.

[@zaraspebongjr.g8937]

Love spot

[@zy.niah13]

I can't understand the pos 2 :((

[@nicksmith4409]

Wonder where the students in the background are today.

[@cheesygaming4072]

the children outside must be have a great time making noise.

[@barnabychicken2202]

“It’s your face”

[@forcircket1537]

proof it A+B=AuB-AnB

[@zephaniahlangley8832]

Do geometry

[@zephaniahlangley8832]

High school

[@chafilalvarez9580]

bye*

[@pratyushbhatt1712]

Oho... The students are just....

[@Hailey-fm1hw]

Yay math lol I was like that was so fake

[@Jehad_Alfayez]

صفوان أبي بكر

[@ItsJustMeStevie]

Must say after a while the videos become annoying. Not so much because of the professor but the students. I must admit you explain more than my current professor but get annoyed after a while. What a shame. Great job though.