Question

If one root of $5x^2+13x+k=0$ is the reciprocal of the other root, then find the value of $k$.

Answer 1

Find the value of $k$.

Let $\alpha$ be one of the roots of the quadratic equation. So, as per the given condition, the other roots is $\frac{1}{\alpha }$.

Product of the roots of quadratic equation is

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

Hence, the value of $k$ is $5.$