Question

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

• A. -64,0
• B. -24,5
• C. 5,-24
• D. 0,72

Answer 1

Answer: (A)

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 $=+8-8=0$