If the roots of the equation

Question:

If the roots of the equation $a x^{2}+b x+c=0$ are equal, then then $c=?$

(a) $\frac{-b}{2 a}$

(b) $\frac{b}{2 a}$

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

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

 

Solution:

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

It is given that the roots of the equation $\left(a x^{2}+b x+c=0\right)$ are equal.

$\therefore\left(b^{2}-4 a c\right)=0$

$\Rightarrow b^{2}=4 a c$

$\Rightarrow c=\frac{b^{2}}{4 a}$

 

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