Class JEE Mathematics ALL Q #1151
KNOWLEDGE BASED
APPLY
4 Marks 2026 JEE Main 2026 (Online) 21st January Morning Shift NUMERICAL
The sum of roots of the equation $|x-1|^{2}-5|x-1|+6=0$ is:
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Step-by-Step Solution

Let $y = |x-1|$. The equation becomes $y^2 - 5y + 6 = 0$.

Factoring the quadratic equation, we get $(y-2)(y-3) = 0$.

So, $y = 2$ or $y = 3$.

Case 1: $|x-1| = 2$. This means $x-1 = 2$ or $x-1 = -2$. Thus, $x = 3$ or $x = -1$.

Case 2: $|x-1| = 3$. This means $x-1 = 3$ or $x-1 = -3$. Thus, $x = 4$ or $x = -2$.

The roots are $3, -1, 4, -2$.

The sum of the roots is $3 + (-1) + 4 + (-2) = 4$.

Correct Answer: 4

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to apply their knowledge of absolute value equations and quadratic equations to solve the given problem. They need to manipulate the equation and find the roots.
Knowledge Dimension: PROCEDURAL
Justification: The question requires a specific procedure to solve the equation, involving substitution, solving quadratic equations, and then solving absolute value equations.
Syllabus Audit: In the context of JEE, this is classified as KNOWLEDGE. The question directly tests the student's understanding of solving equations, specifically those involving absolute values and quadratic forms, which is a standard topic in algebra.

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