Question

If one root of polynomial $f\left(x\right)=5x^2+13x+k$ is reciprocal of the other then find the value of k.

Answer 1

$\Rightarrow$ We have, $p\left(x\right)=5x^2+13x+k$

Let first root be $\alpha$, then other root $=\frac{1}{\alpha }$

Now, products of the roots $=\frac{Constantterm}{Coeff.of{x}^2}$

$\Rightarrow$ $\alpha \times \frac{1}{\alpha }=\frac{k}{5}$

$\Rightarrow$ $1=\frac{k}{5}$

$\Rightarrow$ $k=5$