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  4. The product and sum of the roots of the equation |x2|-5|x|-24=0 are respectively

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Q. The product and sum of the roots of the equation $\left|x^{2}\right|-5|x|-24=0$ are respectively

AP EAMCETAP EAMCET 2016

Solution:

Given, $|x|^{2}-5|x|-24=0$
$\Rightarrow |x|^{2}-8|x|+3|x|-24=0$
$\Rightarrow (|x|-8)(|x|+3)=0$
$\Rightarrow |x|=8$ or $|x|=-3$ is rejected.
$\Rightarrow |x|=8$
$\therefore x=\pm 8$
Hence, product of roots $=8 \times(-8)=-64$
and sum of roots $=+8-8=0$