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Roots of a Quadratic Equation

The roots of ...

Question

The roots of the equation $x^{2} + | x | - 2 = 0$ is/are

- 1

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- 2

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1

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2

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Solution

The correct option is C $1$
Given equation can be rewritten as
$| x |^{2} + | x | - 2 = 0 \Rightarrow | x |^{2} + 2 | x | - | x | - 2 = 0 \Rightarrow (| x | + 2) (| x | - 1) = 0 \Rightarrow | x | = 1 (∵ | x | \geq 0)$
$∴ x = - 1, 1$

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