Question

if alpha and beta are the zeros of a polynomial X into x square minus 6 X + K find the value of k such that Alpha square plus beta squared equals to 40

Answer 1

From the polynomial,
$\alpha + \beta = 6 \: \: \: \: \: \alpha \beta = k$
Given,
${ \alpha }^{2} + { \beta }^{2} = 40 \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta = 40 \\ {6}^{2} - 2k = 40 \\ - 2k = 40 - 36= 4 \\ k = - 2$