Question:

The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$ is:

Step-by-Step Solution

Key Concept: Let $t=|x-1|\geq0$: $t^2-5t+6=0\Rightarrow(t-2)(t-3)=0\Rightarrow t=2$ or $t=3$.

Sum of roots $=4$.

Correct Answer: 4