Question

if alpha and beta are the zeroes of quadratic polynomial f(x)= x2-3x-2. find a quadratic polynomial whose zeroes are 1/2alpha+beta and 1/2beta+alpha​

Answer 1

Answer:

let m=1/2 alpha+beta

n =alpha+1/2 beta

x^2-(m+n)x+mn

x^2-(1/2alpha+beta+alpha+1/2beta)x+{(1/2 alpha+beta)(alpha+1/2 beta)}

x^2-(3/2 +alpha+3/2beta)X+(1/2alpha^2++1/2beta^2+5/4alphabeta)