Question

If one root of the quadratic equation $a{x}^2-bx-c=0;a,b,c\in R$ is reciprocal of the other, then which one of the following is correct?

• A. $a=c$
• B. $b=c$
• C. $a+c=0$
• D. $a+b=0$

Answer 1

The correct option is C $a+c=0$

$a{x}^2-bx-c=0;a,b,c\in R$
Since, this is a quadratic equation, so $a\ne 0$.
Let the roots be $\alpha$ and $\frac{1}{\alpha }$.
So, product of roots is,
$\alpha \times \frac{1}{\alpha }=-\frac{c}{a}$
$\Rightarrow a=-c$
$\Rightarrow a+c=0$