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JEE Main 2019 · 8 Apr · Shift I

JEE Main 2019 Mathematics question on Complex Numbers and Quadratic Equations

The sum of the solutions of the equation ∣x−2∣+x(x−4)+2=0|\sqrt{x} - 2| + \sqrt{x}(\sqrt{x} - 4) + 2 = 0 (x>0)(x > 0) is equal to
  1. A.
    9
  2. B.
    12
  3. C.
    4
  4. D.
    10
Show answer and solution

Correct option: D

Solution

Let t = √x (t > 0). The equation becomes |t - 2| + t(t - 4) + 2 = 0, i.e., |t - 2| + t² - 4t + 2 = 0.

Case 1: t ≥ 2 → (t - 2) + t² - 4t + 2 = 0 → t² - 3t = 0 → t(t - 3) = 0 → t = 3 (since t > 0), giving x = 9.

Case 2: t < 2 → (2 - t) + t² - 4t + 2 = 0 → t² - 5t + 4 = 0 → (t-1)(t-4) = 0 → t = 1 (since t < 2), giving x = 1.

Sum of solutions = 9 + 1 = 10.

[JEE Main 2019 · 8 Apr · Shift I]

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