Question

If the zeroes of the polynomial
$p(x) = ( {k}^{2} + 4) {x}^{2} + 23x + 4k$
are reciprocals of each other then k=______​

Answer 1

Step-by-step explanation:

The roots are reciprocals. So, their product will be 1.

So, c/a=1.

$\frac{4k}{ {k}^{2} + 4 } = 1 \\ {k}^{2} + 4 = 4k \\ {k}^{2} - 4k + 4 = 0 \\ {(k - 2)}^{2} = 0 \\ k = 2$

Thank you