(B) Given equation is $x^3 - 3x + 2 = 0$. By testing $x = 1$,we get $1^3 - 3(1) + 2 = 1 - 3 + 2 = 0$. So,$(x - 1)$ is a factor. Dividing $x^3 - 3x + 2

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

(B) Given equation is $x^3 - 3x + 2 = 0$. By testing $x = 1$,we get $1^3 - 3(1) + 2 = 1 - 3 + 2 = 0$. So,$(x - 1)$ is a factor. Dividing $x^3 - 3x + 2$ by $(x - 1)$,we get $x^2(x - 1) + x(x - 1) - 2(x - 1) = 0$. $(x - 1)(x^2 + x - 2) = 0$. Factoring the quadratic part: $(x - 1)(x + 2)(x - 1) = 0$. Thus,$(x - 1)^2(x + 2) = 0$. The roots are $1, 1, -2$.

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

Easy

If two roots of the equation $x^3 - 3x + 2 = 0$ are the same,then the roots are:

A
$2, 2, 3$
B
$1, 1, -2$
C
$-2, 3, 3$
D
$-2, -2, 1$

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

If $-1+i$ is a root of the equation $x^4+4x^3+5x^2+2x-2=0$,then the real roots of this equation are

MediumTS EAMCET 2021

View Solution

For what value of $a$ does the curve $y = x^2 + ax + 25$ touch the $x-$axis?

Easy

View Solution

If $f(x) = x^2 + bx + c$ and $f(1+k) = f(1-k)$ for all $k \in R$,for two real numbers $b$ and $c$,then:

MediumTS EAMCET 2025

View Solution

If $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0$,where $a \neq 0$,are

MediumWBJEE 2022

View Solution

If all roots of the equation $x^3 - 2ax^2 + 3bx - 8 = 0$ are positive,where $a, b \in R$,then the minimum value of $b$ is:

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

If two roots of the equation $x^3 - 3x + 2 = 0$ are the same,then the roots are:

Similar Questions

If $-1+i$ is a root of the equation $x^4+4x^3+5x^2+2x-2=0$,then the real roots of this equation are

For what value of $a$ does the curve $y = x^2 + ax + 25$ touch the $x-$axis?

If $f(x) = x^2 + bx + c$ and $f(1+k) = f(1-k)$ for all $k \in R$,for two real numbers $b$ and $c$,then:

If $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0$,where $a \neq 0$,are

If all roots of the equation $x^3 - 2ax^2 + 3bx - 8 = 0$ are positive,where $a, b \in R$,then the minimum value of $b$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module