The root(s) of the quadratic equation $x^{2} - 8 x - 12 = 0$ is/are

4

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6

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2

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8

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Solution

The correct option is C $2$
Given, $x^{2} - 8 x - 12 = 0$
Let $α, β$ be the roots of the equation $a x^{2} + b x + c = 0$
Then $α = \frac{- b + \sqrt{D}}{2 a}$

$β = \frac{- b - \sqrt{D}}{2 a}$
$D = b^{2} - 4 a c$ is the discriminant of the equation.
Here, $D = 64 - 4 (1) (12) = 16$
$\Rightarrow \sqrt{D} = 4$
$α = \frac{8 + 4}{2 \times 1} = 6$
$β = \frac{8 - 4}{2 \times 1} = 2$

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