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JEE Main 202621 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
21 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2026 · 21 January · Morning Shift · Mathematics · Quadratic Equation

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

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

Options

  1. A1
  2. B5
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

Let t=∣x−1∣t = |x-1| where t≥0t \geq 0.
Equation becomes t2−5t+6=0t^2 - 5t + 6 = 0.
(t−2)(t−3)=0(t-2)(t-3) = 0 gives t=2t = 2 or t=3t = 3.
For ∣x−1∣=2|x-1| = 2: x=3x = 3 or x=−1x = -1.
For ∣x−1∣=3|x-1| = 3: x=4x = 4 or x=−2x = -2.
Sum of roots =3+(−1)+4+(−2)=4= 3 + (-1) + 4 + (-2) = 4.
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