Question

If one of the zero of the polynomial
$f(x) = ( {k}^{2} + 4) {x}^{2} + 13x + 4k$
is reciprocal of the other, then find the value of k.​

Answer 1

Answer:

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