Question

If one root of the quadratic equation $a{x}^2+bx+c=0$ is the reciprocal of the other, then

• A. $b=c$
• B. $a=b$
• C. $ac=1$
• D. $a=c$

Answer 1

The correct option is D $a=c$

Given quadratic equation is $a{x}^2+bx+c=0$

Let $\alpha$ and $\beta$ be the roots of the equation.
It is given that $\alpha =\frac{1}{\beta }$

Now, $\alpha \beta =\frac{c}{a}$

$\therefore \frac{c}{a}=1$
Hence, $c=a$