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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

A

- 1

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B

- 2

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C

1

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D

2

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Solution

The correct options are
A $- 1$
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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Roots of a Quadratic Equation

Standard XIII Mathematics

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