Question

If alpha and beta are the zeroes of polynomial x^2-px+36 and alpha^2+beta^2=9, then what is the value of p ?

Answer 1

$from \: the \: polynomial \\ \alpha + \beta = p \: \: \: \: \: \: \: \alpha \beta = 36$
$given \\ { \alpha }^{2} + { \beta }^{2} = 9 \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta = 9 \\ {p}^{2} - 2 \times 36 = 9 \\ {p}^{2} = 81 \\ p = + 9 \: \: or \: \: - 9$