Question

If alpha and beta are the zeroes of the polynomial x^2+6x+q then form a polynomial whose zeroes are -alpha and -beta

Answer 1

$p(x) = {x}^{2} + 6x + q \\ \alpha + \beta = - \frac{b}{a} = - 6 \\ \alpha \beta = \frac{c}{a} = q \\ - \alpha - \beta = - ( \alpha + \beta ) = - ( - 6) = 6 = - \frac{b}{a} \\ ( - \alpha )( - \beta ) = q = \frac{c}{a} \\ required \: polynomial = {x}^{2} - 6x + q$