Question

If one of the zeroes of polynomial x2 - kx +16 is cube of other then find value of k

Answer 1

let one zero be
$\alpha$
then other will be
${ \alpha }^{3} \\ \alpha + { \alpha }^{3} = k \\ \alpha \times { \alpha }^{3} = 16 \\ { \alpha }^{4} = {2}^{4} \\ \alpha = 2 \\ 2 + {2}^{3} = k \\ 2 + 8 = k \\ k = 10$