Question

The number of real solutions of \( x^{2} - 3|x| + 2 = 0 \) is:

• A. 2
• B. 4
• C. 1
• D. 3

Hint:

Equations involving $|x|$ are often symmetric; if $x$ is a solution, $-x$ is usually also a solution.

Answer 1

The Correct Option is B

Step 1: Concept
Note that $x^{2} = |x|^{2}$. The equation is a quadratic in $|x|$.
Step 2: Analysis
$|x|^{2} - 3|x| + 2 = 0 \Rightarrow (|x|-1)(|x|-2) = 0$.
$|x| = 1$ or $|x| = 2$.
Step 3: Conclusion
From $|x|=1$, $x = \pm 1$. From $|x|=2$, $x = \pm 2$. Total 4 solutions.
Final Answer: (B)