Question

If the roots of the equation $a{x}^2+bx+c=0$ are equal, then then c = ?
(a) $\frac{-b}{2a}$
(b) $\frac{b}{2a}$
(c) $\frac{-b^2}{4a}$
(d) $\frac{b^2}{4a}$

Answer 1

(d) $\frac{b^2}{4a}$

$$\begin{gathered} \text{It is given that the roots of the equation (}a{x}^2\text{+}bx+c=0)\text{are equal.} \\ \therefore (b^2-4ac)=0 \\ \Rightarrow b^2=4ac \\ \Rightarrow c=\frac{b^2}{4a} \end{gathered}$$