Question

If alpha and beta are the zeros of the quadratic polynomial ax2+bx+c then find the value of alpha square + beta square

Answer 1

this is the answer hope it helps

Answer 2

The required value is

$\alpha^2 + \beta^2=\dfrac{b^2-2ac}{a^2}$

Step-by-step explanation:

We are given the following in the question:

$\alpha, \beta$ are the roots of the equation:

$ax^2+bx+c\\\\=x^2 + \dfrac{b}{a}x + \dfrac{c}{a}$

The general form of equation can be written as:

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

Comparing we get,

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

We have to find the value of

$\alpha^2 + \beta^2 = (\alpha+\beta)^2-2\alpha\beta\\\\\alpha^2 + \beta^2=(-\dfrac{b}{a})^2-2(\dfrac{c}{a})\\\\\alpha^2 + \beta^2=\dfrac{b^2-2ac}{a^2}$

#LearnMore

If alpha and beta are the zeros of the quadratic polynomial f of x is equal to x square - 4 x + 3 find the value of Alpha square beta + alpha beta square

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