Question

If one root of the equation 5x² +13x + k = 0 is the reciprocal of the other root then find the value of k.

Answer 1

Let one root be $\alpha$ and the other root be $\frac{1}{\alpha }$.

The given equation is 5x² +13x + k = 0.

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

Hence, the value of k is 5.