Question

Very-Short-Answer Questions

If one root of the quadratic equation $3x^2-10x+k=0$ is reciprocal of the other, find the value of k. [CBSE 2014]

Answer 1

Let $\alpha$ and $\beta$ be the roots of the equation $3x^2-10x+k=0$.
$\therefore \alpha =\frac{1}{\beta }$ (Given)
$$\begin{gathered} \Rightarrow \alpha \beta =1 \\ \Rightarrow \frac{k}{3}=1\left(\mathrm{Product}\mathrm{of}\mathrm{the}\mathrm{roots}=\frac{c}{a}\right) \\ \Rightarrow k=3 \end{gathered}$$

Hence, the value of k is 3.