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JEE Main 202624 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
24 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Main 2026 · 24 January · Morning Shift · Mathematics · Basics of Mathematics

The number of the real solutions of the equation: x|x+3|+|x-1|-2=0...

The number of the real solutions of the equation: x∣x+3∣+∣x−1∣−2=0x|x+3|+|x-1|-2=0 is

Options

  1. A2
  2. B4
  3. C3
  4. D5

Correct answer

C. 3

Step-by-step solution

Critical points: x=−3x=-3 and x=1x=1.
Case x<−3x < -3:
x2+4x+1=0⇒x=−2±3x^2+4x+1=0 \Rightarrow x=-2\pm\sqrt{3}.
Only x=−2−3≈−3.73x=-2-\sqrt{3} \approx -3.73 lies in (−∞,−3)(-\infty,-3). (1 solution)
Case −3≤x<1-3 \le x < 1:
x2+2x−1=0⇒x=−1±2x^2+2x-1=0 \Rightarrow x=-1\pm\sqrt{2}.
Both x=−1+2≈0.41x=-1+\sqrt{2} \approx 0.41 and x=−1−2≈−2.41x=-1-\sqrt{2} \approx -2.41 lie in [−3,1)[-3,1). (2 solutions)
Case x≥1x \ge 1:
x2+4x−3=0⇒x=−2±7x^2+4x-3=0 \Rightarrow x=-2\pm\sqrt{7}.
Neither root ≥1\ge 1. (0 solutions)
Total number of real solutions =3= 3.
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