Question

If one root of $5x^2+13x+k=0$ be the reciprocal of the other root, then the value of k is
(a) 0
(b) 1
(c) 2
(d) 5

Answer 1

(d) 5
$$\begin{gathered} \text{Let the roots of the equation (5}{x}^2\text{+ 13}x+k=0)\text{be}\alpha \text{and}\frac{1}{\alpha }\text{.} \\ \therefore \text{Product of the roots =}\frac{c}{a} \\ \Rightarrow \alpha \times \frac{1}{\alpha }=\frac{k}{5} \\ \Rightarrow 1=\frac{k}{5} \\ \Rightarrow k=5 \end{gathered}$$