Sum and Product of Roots | Symmetrical Functions of root

By symmetric function of roots, we mean that the function remains unchanged when the roots are interchanged.
Let α and β be the roots.
A function in α and β is said to be a symmetric function if the function remains the same when α and β are interchanged.
Consider α+β. When α is written as β, and β is written as α, the function becomes β+α, which is same as α+β.
So α+β is a symmetric function of the roots.
αβ is also a symmetric function of the roots as αβ = βα
α-β is not a symmetric function as α-β is not equal to β-α unless if β=α
However, mod(α-β) is a symmetric function, as mod(α-β )= mod(β-α)
Value of a #symmetric #function of the #roots in terms of the coefficients of the quadratic equation
α +β = -b/a
αβ = c/a
See Proof: • Relationship Between R...
Value of a symmetric function of α and β can be obtained if α+β and αβ are known.
To find the value of the symmetric function of the roots, express the given function in terms of α+β and αβ.
You can use the following results:
α²+β² = (α +β)² - 2αβ
α³+β³ = (α +β)³ - 3αβ(α+β)
α⁴+β⁴ = (α³+β³)(α +β)-αβ(α²+β²)
(α+β)⁴= α⁴+6α³β+4α²β²+6αβ³+β⁴
= α⁴+β⁴+6αβ(α²+β²)+4α²β²
α⁵+β⁵ = (α³+β³)(α²+β²)-(α²β³+α³β²)
=(α³+β³)(α²+β²)-(α²β²)(α+β)
mod(α -β ) = √[(α +β)²-4αβ]
α²-β²= (α+β)(α-β)
α³-β³ = (α-β)³+3αβ(α-β)
= (α-β)[(α +β)²-αβ]
α⁴-β⁴ = (α²+β²)(α²-β²)
= (α+β)(α-β)(α²+β²)
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[@francisnjie4124]

I appreciate your work deeply sir, it's realy been helpful. Please could you make this clear: you (a ^2+ B ^2), when you were done expanding, how did a minus sign come before the 2aB ?

[@pipslord001]

In the first question... The third line were the parenthesis was expanded ... U used -2 instead of +2 ...can u be clear about that?

[@robinsonmugala127]

wow....i got what have been looking at...solving sam of pefect roots....

[@TiwaElise]

How do we make the product of the second problem

[@tinodaisheganyani7178]

Your teaching sir is much understandable .Keep doing such good work

[@tambuwalmathsclass]

Thank you 🙏

[@musondamwenya7001]

Job well done ✅ thanks alot

[@mapenzihamoomba8749]

Great videos sir👏🏾….appreciation from Zambia 🇿🇲😃

[@tambuwalmathsclass]

Thank you

[@rahmatbadamasi5792]

Thanks so much more knowledge. I have really learn a lot jazakhallahu khairan.

[@tambuwalmathsclass]

Ameen 🙏

[@noahmuke7281]

Watching all the way from Ndola

[@mariamadibbasey4069]

Is understandable, thanks so much

[@tambuwalmathsclass]

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Thank you sir ✨

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THANK YOUU SO MUCHH

[@tambuwalmathsclass]

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[@noahmuke7281]

Thank you so much sir

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Sir watching from India

[@aamirjamal7659]

Nice teaching 👍 👌

[@thegreatkiller375]

I really understand its terms

[@Madepabiayera]

You are a Good teacher You teaches well❤

[@tambuwalmathsclass]

Thank you

[@damolashe]

Thank you very much

[@tambuwalmathsclass]

Welcome

[@onileyanomotoyosi5360]

Thank you for your teachings Allah bless you Please do you know any study group for secondary school, science students Thank you

[@ayodejidara5283]

Thanks!!

[@tambuwalmathsclass]

🙏🙏

[@mohammedrafiq7419]

Masha Allah

[@binibrahim590]

Assalam Alaikum warahmatullah. Masha Allah, this is really great and enjoyable tutorial. I have a question by the way. In solving for the 3rd question, can we just make it simple by substituting the values in the first step where it says (á+ɓ)(á+ɓ)²

[@tambuwalmathsclass]

No because we want to find a³+b³ not (a+b)³ they are never the same

[@binibrahim590]

@@tambuwalmathsclass Ok I get it. Thanks. jazakumullahu Khair

[@boladavid8238]

thanks alot

[@tambuwalmathsclass]

🙏🙏

[@mukhtarullah8590]

Sir please help me lot of because my chemistry exame is near solve this question underoot (x+b/x-b)find Dy/Dx

[@Nsikak-abasiEbong-ex4tk]

Please 🙏🥺 help me to solve the root product of question b Cause it's only the sum product u solved

[@cosmasmali]

Can you please express alpha squared minus beta squared????

[@tambuwalmathsclass]

I have done that already

[@samirzain7212]

Mashallah tnx bro I really understood well

[@tambuwalmathsclass]

👍👍👍 Great

[@samirzain7212]

@@tambuwalmathsclass if the roots of the equation X2-5x-7=0 are alpha and beta. Find the equation whose roots are a) alfa-2,beta-2) b) 1 out of alfa,1 out of beta) c) alfa out of beta, beta out of alfa. Plz help me do this questions give me hints.

[@tambuwalmathsclass]

Isn't it supposed to be (alpha-2) + (Beta-2)?

[@samirzain7212]

@@tambuwalmathsclass it is (alpha-2,beta-2) it is like that

[@maryojo6732]

Pls can you make a video on cubic root

[@tambuwalmathsclass]

Sure

[@PF_BUCHI]

Please can you solve for alpha minus beta

[@tambuwalmathsclass]

I've done that already

[@myyoutube5237]

love from🇮🇳

[@hotcode6796]

This is great... Keep up the good work sir

[@tambuwalmathsclass]

Thanks 🙏

[@DavidSebastine]

❤

[@aamirjamal7659]

Love ❤ 😍 from Bihar India 🇮🇳 ❤ 😍

[@tambuwalmathsclass]

Thank you

[@FortuneMayonde]

It's not helping

[@dabraghabubagha4243]

Alpha²+beta²=(alpha+beta)-2(alpha×beta) Not: Alpha²+beta²=(alpha+beta)+2(alpha×beta)

[@tambuwalmathsclass]

I've not written anything as such, in fact all the two Equations you have written are wrong

[@DavidSebastine]

❤

[@DavidSebastine]

❤