Question

The equation $x^2-3\left|x\right|+2=0$ has

• A. No real roots
• B. One real root
• C. Two real roots
• D. Four real roots

Answer 1

Answer: (D)

Four real roots

Since, $x^2-3\left|x\right|+2=0$
$\Rightarrow \left|x^2\right|-2\left|x\right|-\left|x\right|+2=0$
$\Rightarrow (\left|x\right|-2)(\left|x\right|-1)=0$
$\Rightarrow \left|x\right|=2$ or $\left|x\right|=1$
$\Rightarrow x=\pm 2$ or $x=\pm 1$
$\therefore$ The given equation has four real roots.