Question

Find the condition that one of roots of $a{x}^2+bx+c=0$ may be reciprocal of the other.

Answer 1

Let, the roots of $a{x}^2+bx+c=0$ be $\alpha and\frac{1}{\alpha }.$

$\because$ Product of roots $=\frac{c}{a}$

i.e., $\alpha \times \frac{1}{\alpha }=\frac{c}{a}$

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

$\therefore a=c$

This is our required condition.