(D) Given the equation $|x|^2 - 3|x| + 2 = 0$.Let $|x| = t$,where $t \ge 0$.The equation becomes $t^2 - 3t + 2 = 0$.Factoring the quadratic equation:

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(D) Given the equation $|x|^2 - 3|x| + 2 = 0$.Let $|x| = t$,where $t \ge 0$.The equation becomes $t^2 - 3t + 2 = 0$.Factoring the quadratic equation: $(t - 1)(t - 2) = 0$.This gives $t = 1$ or $t = 2$.Since $t = |x|$,we have $|x| = 1$ or $|x| = 2$.For $|x| = 1$,the solutions are $x = 1$ and $x = -1$.For $|x| = 2$,the solutions are $x = 2$ and $x = -2$.Thus,the real solutions are $x \in \{1, -1, 2, -2\}$.The total number of real solutions is $4$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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The number of real solutions of the equation $|x|^2 - 3|x| + 2 = 0$ is

AIEEE 2003 All AIEEE

IIT 1982 All IIT

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A
$1$
B
$2$
C
$3$
D
$4$

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