The number of solutions of the equation ${| x |}^{2} - 3 | x | + 2 = 0$ is

4

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2

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0

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1

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Solution

The correct option is A $4$
$| x |^{2} - 3 | x | + 2 = 0$
$(| x | - 2) (| x | - 1) = 0$
$| x | = 2$ and $| x | = 1$
This gives us
$| x | = \pm 2$ and $| x | = \pm 1$
Hence
$x = - 2, - 1, 1, 2$ .
Thus there are in total 4 roots.

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