The sum of real roots of the equation $x^{2} + | x | - 6 = 0$ is

4

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0

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- 1

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none of these

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Solution

The correct option is D $0$
We have to consider two cases when $x \geq 0$ and $x < 0$
Case (1) When $x \geq 0$
$x^{2} + x - 6 = 0$
$(x - 2) (x + 3) = 0$
$x = 2$ or $x = - 3$ (neglected as $x > 0$ )
Case (2) When $x < 0$
$x^{2} - x - 6 = 0$
$(x + 2) (x - 3) = 0$
$x = - 2$ or $x = 3$ (neglected as $x < 0$ )
So, roots are $2$ , $- 2$ and their sum will be zero.

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