Question

The number of real solutions of the equation ${\left|x\right|}^2-3\left|x\right|+2=0$ is

• A. $4$
• B. $1$
• C. $3$
• D. $2$

Answer 1

The correct option is A

$4$

Explanation of correct answer

Given that ${\left|x\right|}^2-3\left|x\right|+2=0$

$$\begin{gathered} \Rightarrow {\left|x\right|}^2-2\left|x\right|-\left|x\right|+2=0 \\ \Rightarrow \left|x\right|\left(\left|x\right|-2\right)-1\left(\left|x\right|-2\right)=0 \\ \Rightarrow \left(\left|x\right|-2\right)\left(\left|x\right|-1\right)=1 \\ \left|x\right|=2,1 \\ \therefore x=1,-1,2,-2 \end{gathered}$$

Hence, the correct option is $\left(\mathrm{A}\right)$.