Question

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

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

Answer: (C)

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