Question

If one root of the quadratic equation 3x² – 10x + k = 0 is reciprocal of the other, then k = ________.

Answer 1

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

The given equation is 3x² – 10x + k = 0.

Product of roots = $\frac{k}{3}$
$$\begin{gathered} \Rightarrow \alpha \times \frac{1}{\alpha }=\frac{k}{3} \\ \Rightarrow 1=\frac{k}{3} \\ \Rightarrow k=3 \end{gathered}$$

Hence, k = 3.