If $a x^{2} + b x + c = 0$ has equal roots, find the value of $c$ .

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Solution

# $a x^{2} + b x + c = 0$ has equal root then
$B^{2} - 4 A C = 0$ $A = a$ $B = b$ $C = c$
$\Rightarrow b^{2} - 4 a c = 0 \Rightarrow 4 a c = b^{2}$
$C = \frac{b^{2}}{4 a}$

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