Question
The number of the real solutions of the equation: x|x+3|+|x-1|-2=0 is
JEE Main
Mathematics
Basic of Mathematics
2026
JEE Main 2026 (24 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2
- B. 4
- C. 3
- D. 5
Answer
C. 3
Step-by-step solution
Critical points: x=-3 and x=1. Case x x^2+4x+1=0 x=-2 3 . Only x=-2- 3 -3.73 lies in (- ,-3). (1 solution) Case -3 x x^2+2x-1=0 x=-1 2 . Both x=-1+ 2 0.41 and x=-1- 2 -2.41 lie in [-3,1). (2 solutions) Case x 1: x^2+4x-3=0 x=-2 7 . Neither root 1. (0 solutions) Total number of real solutions = 3.
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