Question

if alfa and beta are the zeroes of the quadratic polynomial ax2+bx+c then evaluate alfa square + beta square

Answer 1

here is the answer.
hope its clear

Answer 2

Given equation :- ax² + bx + c

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

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


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

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




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


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