(A) Let $|x-1|=t$. Then the equation becomes $t^{2}-5t+6=0$. Factoring the quadratic equation, we get $(t-2)(t-3)=0$, so $t=2$ or $t=3$. Case $1$: $|x

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) Let $|x-1|=t$. Then the equation becomes $t^{2}-5t+6=0$. Factoring the quadratic equation, we get $(t-2)(t-3)=0$, so $t=2$ or $t=3$. Case $1$: $|x-1|=2 \implies x-1=2$ or $x-1=-2$, which gives $x=3$ or $x=-1$. Case $2$: $|x-1|=3 \implies x-1=3$ or $x-1=-3$, which gives $x=4$ or $x=-2$. The roots are $3, -1, 4, -2$. The sum of the roots is $3 + (-1) + 4 + (-2) = 4$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

Difficult

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

JEE MAIN 2026 All JEE MAIN

A
$4$
B
$3$
C
$1$
D
$5$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-2.Quadratic Equations and Inequations

Subtopic

Solution of quadratic equations and Nature of roots

Previous Year

JEE MAIN 2026 Paper All JEE MAIN years →

Let $p, q, r \in \mathbb{R}$ and $r > p > 0.$ If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta,$ then $|\alpha| + |\beta|$ is:

DifficultAIEEE 2012

View Solution

The roots of the equation $\sqrt{3x + 1} + 1 = \sqrt{x}$ are

Easy

View Solution

If $3$ is a root of the equation $x^2 + kx - 24 = 0$,then $3$ is also a root of which of the following equations?

Medium

View Solution

The smallest positive integral value of $a$, for which all the roots of $x^4 - ax^2 + 9 = 0$ are real and distinct, is equal to

DifficultJEE MAIN 2026

View Solution

If $1$ is a multiple root of order $3$ for the equation $x^4-2x^3+2x-1=0$,then the other root is

MediumTS EAMCET 2001

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

Let $p, q, r \in \mathbb{R}$ and $r > p > 0.$ If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta,$ then $|\alpha| + |\beta|$ is:

The roots of the equation $\sqrt{3x + 1} + 1 = \sqrt{x}$ are

If $3$ is a root of the equation $x^2 + kx - 24 = 0$,then $3$ is also a root of which of the following equations?

The smallest positive integral value of $a$, for which all the roots of $x^4 - ax^2 + 9 = 0$ are real and distinct, is equal to

If $1$ is a multiple root of order $3$ for the equation $x^4-2x^3+2x-1=0$,then the other root is

Vedclass Test Series

Exam Paper Generator

Online Exam Module