Question

If the sum of the squares of zeroes of the quadratic polynomial ,
$f(x) = {x}^{2} - 8x + k \:$
is 40. Find the value of k.

Answer 1

$let \: the \: zeroes \: be \: \alpha \: \: and \: \: \beta \\ from \: the \: equation \\ \alpha + \beta = 8 \: \: \: \: \alpha \beta = k \\ given \: \: { \alpha }^{2} + { \beta }^{2} = 40 \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta = 40 \\ {8}^{2} - 2k = 40 \\ k = 12$