Question

if alpha and beta are the zeros of quadratic polynomial f x is equals to ax square + bx + c then evaluate Alpha Cube + beta cube​

Answer 1

hey mate here is your answer

hope it's help you

Answer 2

The required value is

$\alpha^3 + \beta^3= \dfrac{3abc-b^3}{a^3}$

Step-by-step explanation:

We are given the following in the question:

$f(x) = ax^2 + bx +c$

Writing in general form:

$f(x) = x^2 + \dfrac{b}{a}x + \dfrac{c}{a}$

Comparing with

$x^2 - (\alpha + \beta)x + \alpha\beta$

we get:

$\alpha +\beta =-\dfrac{b}{a}\\\\\alpha\beta =\dfrac{c}{a}$

We have to evaluate:

$\alpha^3 + \beta^3 = (\alpha+ \beta)^2 - 3(\alpha + \beta)(\alpha\beta)$

Putting values, we get,

$\alpha^3 + \beta^3 = (-\dfrac{b}{a})^3 - 3(-\dfrac{b}{a})(\dfrac{c}{a})\\\\\alpha^3 + \beta^3= \dfrac{-b^3+3abc}{a^3}\\\\\alpha^3 + \beta^3= \dfrac{3abc-b^3}{a^3}$

which is the required value.

#LearnMore

If alpha and beta are the zeros of the quadratic polynomial f(x)= ax²+bx+c, then evaluate alpha/beta + beta/Alpha

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