Question

The roots of the equation $a{x}^2+bx+c=0$ will be reciprocal of each other if
(a) a = b
(b) b= c
(c) c = a
(d) none of these

Answer 1

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