Question

Find the condition that the roots of the equation $a{x}^2+bx+c=0$ be such that
Both roots are equal

Answer 1

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

Applying quadratic formula,

$⟹\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}⟹2\sqrt{b^2-4ac}=0⟹\sqrt{b^2-4ac}=0⟹b^2=4ac⟹b=\pm \sqrt{4ac}⟹b=\pm 2\sqrt{ac}\therefore b=\pm 2\sqrt{ac}$