Question

if alpha and beta are two zeroes of the polynomial x²-pq+q find another polynomial whose zeroes are 2alpha/beta, 2beta/alpha​

Answer 1

Answer:

how

Step-by-step explanation:

f(x)=x2+px+q

Roots are α and β

α+β=−p

αβ=q

(α+β)2=p2

(α−β)2=(α+β)2−4αβ

p2−4q

New Roots are (α+β)2 and (α−β)2

Sum=(α+β)2 + (α−β)2

=p2+p2−4q

=2(p2−2q)

Product=(α+β)2 (α−β)2

=p2(p2−4q)

∴f(x)=K(x2−2(p2−2q)x+p2(p2−4q))