Question

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

Answer 1

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

$\because$ Sum of roots $=\frac{-b}{a}$

I.e., $\alpha +(-\alpha )=\frac{-b}{a}$

$⟹0=\frac{-b}{a}$

$⟹0=-b$

$\therefore b=0$

This is our required condition.