Question

If zeros of the polynomial are alpha and beta f(x)=x2-p(x+1)-x find alpha 2 beta *beta 2alpha

Answer 1

$given \: polynomial \: is \: x {}^{2} - p(x + 1) - x \\ \\ = x ^{2} - px - p - x \\ \\ = x {}^{2} - (p + 1)x - p \\ \\ let \: \alpha \: and \: \beta are \: the \: roots \: of \: the \: polynomial \\ \\ therefore \: product \: of \: the \: roots \: is \: \alpha \beta = \frac{ - p}{1 } \\ \\ = - p \\ \\ therefore \: \alpha {}^{2} \beta \times \beta {}^{2} \alpha = \alpha {}^{3} \beta {}^{3 } \\ \\ = ( \alpha \beta ) {}^{3} = ( - p) {}^{3} = - p ^{3}$
hope it helps