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  4. The number of real roots of |x|2-5|x|+6=0 is

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Q. The number of real roots of $|x|^{2}-5|x|+6=0$ is

TS EAMCET 2016

Solution:

We have,
$|x|^{2}-5|x|+6=0$
Let $|x|=y$
$\Rightarrow y^{2}-5 y+6=0$
$\Rightarrow (y-2)(y-3)=0$
$\Rightarrow y=2,3$
$\Rightarrow |x|=2$ or $|x|=3$
$x=\pm 2$ or $\pm 3$
$ \therefore $ Number of real roots are $4$