Maths Question :) (Class 10)
If α and β are the zeros of the polynomial f(x)=ax²+bx+c,then evaluate
(i)(β/aα+b)+(α/aβ+b)
(ii)a(α²/β+β²/α)+b(α/β+β/α)
Anonymous:
I don't want any complicated answer :)
is it from textbook
naahh..! xD
from where
You can not copy and answer @Ankitakumari
It is from refresher ..! But sorry I will not tell any name
Mai answer du
I know it
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f(x) = a x² + b x + c
⇒ α+b = -b/a αβ = c/a
⇒ α²+β² = b²/a² - 2c/a = (b² - 2ac) / a²
⇒ α³ + β³ = (α+β)³ - 3αβ(α+β) = - b³/a³ + 3cb / a² = b(3ac-b²)/a³
1)
2)
![a(\frac{\alpha^2}{\beta}+\frac{\beta^2}{\alpha})+b(\frac{\alpha}{\beta}+\frac{\beta}{\alpha})\\\\=\frac{1}{\alpha\beta}[a(\alpha^3+\beta^3)+b(\alpha^2+\beta^2)]\\\\=\frac{a}{c} \frac{1}{a^2} [ 3abc-b^3+ b^3-2abc ]\\\\=a^2bc/a^2c\\\\=b](https://tex.z-dn.net/?f=a%28%5Cfrac%7B%5Calpha%5E2%7D%7B%5Cbeta%7D%2B%5Cfrac%7B%5Cbeta%5E2%7D%7B%5Calpha%7D%29%2Bb%28%5Cfrac%7B%5Calpha%7D%7B%5Cbeta%7D%2B%5Cfrac%7B%5Cbeta%7D%7B%5Calpha%7D%29%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B%5Calpha%5Cbeta%7D%5Ba%28%5Calpha%5E3%2B%5Cbeta%5E3%29%2Bb%28%5Calpha%5E2%2B%5Cbeta%5E2%29%5D%5C%5C%5C%5C%3D%5Cfrac%7Ba%7D%7Bc%7D+%5Cfrac%7B1%7D%7Ba%5E2%7D+%5B+3abc-b%5E3%2B+b%5E3-2abc+%5D%5C%5C%5C%5C%3Da%5E2bc%2Fa%5E2c%5C%5C%5C%5C%3Db "a(\frac{\alpha^2}{\beta}+\frac{\beta^2}{\alpha})+b(\frac{\alpha}{\beta}+\frac{\beta}{\alpha})\\\\=\frac{1}{\alpha\beta}[a(\alpha^3+\beta^3)+b(\alpha^2+\beta^2)]\\\\=\frac{a}{c} \frac{1}{a^2} [ 3abc-b^3+ b^3-2abc ]\\\\=a^2bc/a^2c\\\\=b")
⇒ α+b = -b/a αβ = c/a
⇒ α²+β² = b²/a² - 2c/a = (b² - 2ac) / a²
⇒ α³ + β³ = (α+β)³ - 3αβ(α+β) = - b³/a³ + 3cb / a² = b(3ac-b²)/a³
1)
2)
Sir,There is a blank space in second answer :(
done
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