Question

If one zero of the polynomial f(x) = ( k^2 + 4 ) x^2 + 13x + 4k is the reciprocal of the other then k =

Answer 1

let one zero be α then the other will be 1/α
clearly from the above step we can see that the product of the roots is 1 so c/a=1
4k/k²+4=1

4k=k²+4
k²-4k+4=0
(k-2)(k-2)
hence k=2