1. The sum of all roots of the equation $(x – 1)^2 – 5|x – 1| + 6 = 0$ is:
a) 4
b) 1
c) 5
d) 3
(JEE Main 2026 | Exam Date: 21.01.2026 | Shift I)
Answer: (a) 4
Solution: Let $|x – 1| = t$. The equation becomes $t^2 – 5t + 6 = 0$. Solving for $t$:
$$(t – 2)(t – 3) = 0 \Rightarrow t = 2, 3$$
If $|x – 1| = 2$, then $x – 1 = 2$ or $x – 1 = -2$, giving $x = 3, -1$.
If $|x – 1| = 3$, then $x – 1 = 3$ or $x – 1 = -3$, giving $x = 4, -2$.
Sum of roots: $3 + (-1) + 4 + (-2) = 4$.