Question
The sum of all the real solutions of the equation _ (x+3) (6 x^ 2 +28 x+30 )=5-2 _ (6 x+10) (x^ 2 +6 x+9 ) is equal to
JEE Main
Mathematics
Quadratic Equation
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2
- B. 1
- C. 0
- D. 4
Answer
C. 0
Step-by-step solution
Note 6x^2+28x+30 = 2(3x+5)(x+3), x^2+6x+9 = (x+3)^2, 6x+10 = 2(3x+5). Let a = _ (x+3) [2(3x+5)]. Then LHS = a + 1 and _ 2(3x+5) (x+3)^2 = 2 a . Equation becomes a + 1 = 5 - 4 a , i.e., a^2 - 4a + 4 = 0 a = 2. So _ (x+3) [2(3x+5)] = 2 (x+3)^2 = 6x+10 x^2 = 1 x = 1 or x = -1. Both satisfy domain conditions (bases > 0, 1; arguments > 0). Sum = 1 + (-1) = 0.
Related: Mathematics — Quadratic Equation · All PYQ Banks