Question
The number of distinct real solutions of the equation x|x+4|+3|x+2|+10=0 is
JEE Main
Mathematics
Functions
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2
- B. 1
- C. 3
- D. 0
Answer
B. 1
Step-by-step solution
Equation: x|x+4| + 3|x+2| + 10 = 0. Critical points: x = -4, -2. Case 1: x -2: x(x+4) + 3(x+2) + 10 = 0 x^2+7x+16=0. Discriminant = 49-64 = -15 Case 2: -4 x x^2+x+4=0. Discriminant = 1-16 = -15 Case 3: x x^2+7x-4=0. x = -7 65 2 . x = -7+ 65 2 0.53 (rejected, not in x Number of distinct real solutions = 1.
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