Question

If one zero of polynomial (k*2+16)x*2 +13x+8k is reciprocal of the other find k

Answer 1

Let one zero be alpha, therefore the other zero is (1/alpha).
Now we know that
$\alpha \beta = \frac{c}{a}$
In this case
$\alpha \times \frac{1}{ \alpha } = \frac{8k}{ {k}^{2} + 16} \\ 1 = \frac{8k}{ {k}^{2} + 16 } \\ {k}^{2} - 8k + 16 = 0 \\ {(k - 4)}^{2} = 0 \\ k = 4$