Question

If Alfa and beta are the zeroes of the quadratic polynomial f(x) = kx² + 4x + 4 such that Alfa² + beta² = 24 find the value of k

Answer 1

let alpha =a and beta=b
a+b= -4/k and ab= 4/k
a^2+b^2=[(a+b)^2-2ab]
24=16/k^2 - 8/k
3=2/k^2 - 1/k
3k^2+k-2=0
(3k-2)(k+1)=0
k = 2/3 or -1