Question
The sum of all the roots of the equation (x-1)^ 2 -5|x-1|+6=0, is :
JEE Main
Mathematics
Quadratic Equation
2026
JEE Main 2026 (21 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 1
- B. 5
- C. 3
- D. 4
Answer
D. 4
Step-by-step solution
Let t = |x-1| where t 0. Equation becomes t^2 - 5t + 6 = 0. (t-2)(t-3) = 0 gives t = 2 or t = 3. For |x-1| = 2: x = 3 or x = -1. For |x-1| = 3: x = 4 or x = -2. Sum of roots = 3 + (-1) + 4 + (-2) = 4.
Related: Mathematics — Quadratic Equation · All PYQ Banks