Question

If alpha and bita are the zeros of the quadratic polynomial f(x) = bx² + 4x + 4 such that
a2 + B2 = 24, find the values of k.​

Answer 1

Step-by-step explanation:

α,β roots of f(x)=kx^2+4x+4

α+β=-b/a=-4/k

αβ=c/a=4/k

We know that,

(α+β)^2=α^2+β^2+2αβ

On substituting and solving,

3k^2+k-2=0

k=-1,2/3.

This is the required answer.