Find the roots of the quadratic equation $a x^{2} + b x + c = 0$ in terms of a, b, c.

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Solution

The correct option is A

$a x^{2} + b x + c = 0 (a \neq 0)$
Diving throughout by a
$x^{2} + \frac{b}{a} x + \frac{c}{a} = 0$
$\Rightarrow {(x + \frac{b}{2 a})}^{2} - {(\frac{b}{2 a})}^{2} + \frac{c}{a} = 0 \Rightarrow {(x + \frac{b}{2 a})}^{2} - \frac{b^{2} - 4 a c}{4 a^{2}} = 0 \Rightarrow (x + \frac{b}{2 a}) = \pm \sqrt{\frac{b^{2} - 4 a c}{4 a^{2}}} = \frac{\pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- b}{2 a} \pm \frac{\sqrt{b^{2} - 4 a c}}{2 a}$

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Similar questions

Find the roots of the quadratic equation $a x^{2} + b x + c$ in terms of a, b, c

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