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Absolute Value Function

If x|x|+3|x|-...

Question

If $x | x | + 3 | x | - 10 = 0$ , then $x =$

0

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2

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- 5

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- 2

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Solution

The correct option is B $2$
$x | x | + 3 | x | - 10 = 0$
When $x \geq 0$
$x^{2} + 3 x - 10 = 0$
$\Rightarrow (x + 5) (x - 2) = 0$
$\Rightarrow x = 2$ or $x = - 5$ which is absurd.

When $x < 0$
$- x^{2} - 3 x - 10 = 0$
As $D < 0$ hence, no solution.

$∴ x = 2$

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