The number of real solutions of the equation, $x^{2} - | x | - 12 = 0$ is

4

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1

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2

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3

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Solution

The correct option is C $2$
Given: $x^{2} - | x | - 12 = 0$
$\Rightarrow x^{2} - 4 | x | + 3 | x | - 12 = 0$
$\Rightarrow (| x | - 4) (| x | + 3) = 0$
$\Rightarrow | x | = 4$ or $| x | = - 3$ (rejected)
$\Rightarrow x = \pm 4$
$∴$ Number of solutions $= 2$

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