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Standard XII

Mathematics

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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Similar questions

Q. Let

A = {x \in R : x^{2} - | x | - 2 = 0}

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Q. The equation whose roots are the squares of the roots of equation

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Roots of a Quadratic Equation

Standard XII Mathematics

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The roots of the equation x2+|x|−2=0 is/are

The correct option is C 1Given equation can be rewritten as |x|2+|x|−2=0⇒|x|2+2|x|−|x|−2=0⇒(|x|+2)(|x|−1)=0⇒|x|=1 (∵|x|≥0) ∴x=−1,1

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

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