# The roots of the equation

Question:

The roots of the equation $a x^{2}+b x+c=0$ will be reciprocal of each other if

(a) a = b
(b) bc
(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 $=\alpha \times \frac{1}{\alpha}=1$

$\Rightarrow \frac{c}{a}=1$

$\Rightarrow c=a$