Question

If one of the roots of the equation $a{x}^2+bx+c=0$ is reciprocal of the other, choose the correct option.

• A. c = a
• B. $c=a^2$
• C. c = 2a
• D. $a=c^2$

Answer 1

The correct option is A c = a

Let’s assume one of the roots is $\alpha$. If the roots are reciprocal of each other, the other root will be $\frac{1}{\alpha }$
Observe that the product of both the roots is 1 i.e. $\alpha \times \frac{1}{\alpha }=1$ The formula for product of the roots of the quadratic equation is $\frac{c}{a}$.
$\Rightarrow \frac{c}{a}=1$
$\Rightarrow c=a$
Hence the correct option is c = a .