Question:
The number of real solutions of
\( x^{2} - 3|x| + 2 = 0 \)
is:
The number of real solutions of
\( x^{2} - 3|x| + 2 = 0 \)
is:
Show Hint
Equations involving $|x|$ are often symmetric; if $x$ is a solution, $-x$ is usually also a solution.
Updated On: Apr 8, 2026
- 2
- 4
- 1
- 3
Show Solution
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The Correct Option is B
Solution and Explanation
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)
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)
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