The number of real solutions of the equation, x 2 - x - 12 = 0 is:

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Question: Answered & Verified by Expert

The number of real solutions of the equation,

x^{2} - |x| - 12 = 0

is:

MathematicsQuadratic EquationJEE MainJEE Main 2021 (25 Jul Shift 2)

Options:

A $2$
B $3$
C $1$
D $4$

Solution:

1391 Upvotes Verified Answer

The correct answer is:

2

We have, ${|x|}^{2} - |x| - 12 = 0$

$\Rightarrow {|x|}^{2} - 4 |x| + 3 |x| - 12 = 0$

$\Rightarrow (|x| + 3) (|x| - 4) = 0$

$\Rightarrow |x| = 4$ as $|x| \neq - 3$

$\Rightarrow x = \pm 2$

Hence, number of real solution is $2 .$

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