(C) Given the equation $x^{2}-|x|-12=0$.Since $x^{2} = |x|^{2}$,we can rewrite the equation as $|x|^{2}-|x|-12=0$.Let $t = |x|$,where $t \geq 0$. The

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

(C) Given the equation $x^{2}-|x|-12=0$.Since $x^{2} = |x|^{2}$,we can rewrite the equation as $|x|^{2}-|x|-12=0$.Let $t = |x|$,where $t \geq 0$. The equation becomes $t^{2}-t-12=0$.Factoring the quadratic equation: $(t-4)(t+3)=0$.This gives $t=4$ or $t=-3$.Since $t = |x| \geq 0$,we reject $t=-3$.Thus,$|x|=4$,which implies $x=4$ or $x=-4$.Therefore,there are $2$ real solutions.

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

Easy

The number of real solutions of the equation $x^{2}-|x|-12=0$ is:

JEE MAIN 2021 All JEE MAIN

A
$3$
B
$1$
C
$2$
D
$4$

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 2021 Paper All JEE MAIN years →

If $\alpha$ and $\alpha^2$ are the roots of the equation $x^2 + x + 1 = 0$,then the equation whose roots are $\alpha^{31}$ and $\alpha^{62}$ is .....

Medium

View Solution

The product of all the real roots of $x^2-8x+9-\frac{8}{x}+\frac{1}{x^2}=0$ is

EasyTS EAMCET 2017

View Solution

$A$ number is the reciprocal of the other. If the arithmetic mean of the two numbers is $\frac{13}{12}$,then the numbers are:

Easy

View Solution

If the sum of two particular roots of the equation $x^4-4x^3-7x^2+22x+24=0$ is equal to the sum of the remaining two roots,then the sum of the cubes of all the roots of this equation is

MediumTS EAMCET 2023

View Solution

If $\frac{1 + \sqrt{3}i}{2}$ is a root of the equation $x^4 - x^3 + x - 1 = 0$,then its real roots are:

Medium

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 number of real solutions of the equation $x^{2}-|x|-12=0$ is:

Similar Questions

If $\alpha$ and $\alpha^2$ are the roots of the equation $x^2 + x + 1 = 0$,then the equation whose roots are $\alpha^{31}$ and $\alpha^{62}$ is .....

The product of all the real roots of $x^2-8x+9-\frac{8}{x}+\frac{1}{x^2}=0$ is

$A$ number is the reciprocal of the other. If the arithmetic mean of the two numbers is $\frac{13}{12}$,then the numbers are:

If the sum of two particular roots of the equation $x^4-4x^3-7x^2+22x+24=0$ is equal to the sum of the remaining two roots,then the sum of the cubes of all the roots of this equation is

If $\frac{1 + \sqrt{3}i}{2}$ is a root of the equation $x^4 - x^3 + x - 1 = 0$,then its real roots are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module