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

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Solution

Given equation
$| x |^{2} + | x | - 6 = 0 \Rightarrow | x |^{2} + 3 | x | - 2 | x | - 6 = 0 \Rightarrow (| x | + 3) (| x | - 2) = 0 \Rightarrow | x | = 2, | x | = - 3 (not possible)$
$∴ x = \pm 2$

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