Question

if alpha and beta are the zeroes of x 2 - x - 6 find the value of alpha 3+ beta 3

Answer 1

$from \: the \: polynomial \\ \alpha + \beta = 1 \\ \alpha \beta = - 6$

${ \alpha }^{3} + { \beta }^{3} = {( \alpha + \beta )}^{3} - 3 \alpha \beta ( \alpha + \beta ) \\ = {(1)}^{3} - 3 \times - 6 \times 1 \\ = 1 + 18 = 19$