Question

please help me to solve I will mark brainlist

I don't want useless answer​

Answer 1

kindly check the attachment for the stepwise solution and answer.

Answer 2

Step-by-step explanation:

Given equation is

$a {x}^{2} + bx + c = 0$

$sum \: \: of \: \: roots \: \: ( \alpha + \beta ) = - \frac{b}{a}$

$product \: \: of \: \: roots \: \: ( \alpha \beta ) = \frac{c}{a}$

Now,

${ \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta) }^{2} - 2 \alpha \beta$

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

$= > { \alpha }^{2} + { \beta }^{2} = \frac{ {b}^{2} }{ {a}^{2} } + \frac{2c}{a}$

$= > { \alpha }^{2} + { \beta }^{2} = \frac{ {b}^{2} + 2ac }{ {a}^{2} }$