Question

If one zero of polynomial 4xsq.-[8ksq-40k]x-9 is negetive of the other find k

Answer 1

$4 {x}^{2} - (8 {k}^{2} - 40k)x - 9 = 0 \\ roots \: are \: \alpha \: and \: - \alpha \\ \alpha + ( - \alpha ) = \frac{(8 {k}^{2} - 40k)}{4} \\ 0 = 8 {k}^{2} - 40 k\\ 8( {k}^{2} - 5k) = 0 \\ k(k - 5) = 0 \\ k = 0 \: or \: 5$