Question

if alpha and beta are the zeroes of the polynomial f(x) = x^2 + px + q, form a quadratic polynomial whose zeroes are (alpha + beta)^2 and (alpha - beta)^2​

Answer 1

Step-by-step explanation:

let alpha and beta be a and b

a+b= -p

ab =q

a²+pa+q=0, a²=-pa-q

b²+pb+q=0, b²= -pb-q

(a+b)²= -pa-q-pb-q+2q

= -p(a+b)= p²

(a-b)²= -pa-q-pb-q-2q

=p²-4q

sum of roots: 2p²-4q

product of roots: p⁴-4p²q

equation: x²-(2p²-4q)+(p⁴-4p²q)