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JEE Main 1982 Mathematics question on Complex Numbers and Quadratic Equations

The number of real solutions of the equation ∣x∣2−3∣x∣+2=0|x|^2 - 3|x| + 2 = 0 is
  1. A.
    4
  2. B.
    1
  3. C.
    3
  4. D.
    2
Show answer and solution

Correct option: A

Solution

Let u = |x|, so the equation becomes u² - 3u + 2 = 0, which factors as (u-1)(u-2) = 0, giving u = 1 or u = 2. Since u = |x|, each positive value of u gives two real solutions: x = ±1 and x = ±2. This yields 4 real solutions total.

[1982]

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