Question

If alpha and beta are the zeroes of the quadaratic polynomial f(x)x^2-1, find a quadratic polynomial whose zero are 2 alpha/beta and 2beta/alpha

Answer 1

let alpha=a and beta=b
so a+b=0 ab=-1
zeroes of the required polynomial are 2a/b and 2b/a
sum of the zeroes = 2(a^2+b^2)/ab
= 2[(a+b)^2-2ab]/ab
= -4
product of the roots = 4
so the required polynomial is x^2+4x+4