Question:
The roots of the equation $a x^{2}+b x+c=0$ will be reciprocal of each other if
(a) a = b
(b) b= c
(c) c = a
(d) none of these
Solution:
(c) c = a
Let the roots of the equation $\left(a x^{2}+b x+c=0\right)$ be $\alpha$ and $\frac{1}{\alpha}$.
$\therefore$ Product of the roots $=\alpha \times \frac{1}{\alpha}=1$
$\Rightarrow \frac{c}{a}=1$
$\Rightarrow c=a$
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