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

Mathematics · Quadratic Equations

JEE Main 2026 — 21 January, Morning Shift — Question 19

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

Let $|x-1|=t$

$\mathrm{t}^{2}-5 \mathrm{t}+6=0$

$\mathrm{t}=2 \& \mathrm{t}=3$

$|x-1|=2 \&|x-1|=3$

$\mathrm{x}-1 \pm 2 \& \mathrm{x}-1= \pm 3$

$\mathrm{x}=1 \pm 2 \& \mathrm{x}=1 \pm 3$

∴ root $=3,-1,4,-2$

∴ Sum of root $=3+(-1)+4+(-2)=4$ .

Answer key and solution verified before publishing.

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.