Question

If alpha and beta are the zeros of the polynomial x^2-2x+1, then find the quadratic polynomial, whose zeroes are 2 alpha/beta and 2 beta/alpha

Answer 1

from eqn
α+β=2
.αβ=1
if roots are 2α/β and 2β/α
sum=2(α/β+β/α)=2(α^2+β^2/αβ)
α^2+β^2=(α+β)^2-2αβ=2
sum=s=2(2)/1=4
product=p=4
eqn
x^2-sx+p=0
x^2-4x+4=0