(C) Given the equation ${t^2}{x^2} + |x| + 9 = 0$. For any real number $t$ and $x$,we know that ${t^2}{x^2} \ge 0$ and $|x| \ge 0$. Therefore,${t^2}{x

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

(C) Given the equation ${t^2}{x^2} + |x| + 9 = 0$. For any real number $t$ and $x$,we know that ${t^2}{x^2} \ge 0$ and $|x| \ge 0$. Therefore,${t^2}{x^2} + |x| + 9 \ge 9$. Since the expression is always greater than or equal to $9$,it can never be equal to $0$. Thus,the equation has no real roots. Consequently,the product of the real roots does not exist.

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

Easy

What is the product of the real roots of the equation ${t^2}{x^2} + |x| + 9 = 0$?

AIEEE 2002 All AIEEE

A
Is always positive
B
Is always negative
C
Does not exist
D
None of these

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

AIEEE 2002 Paper All AIEEE years →

If $x^2+x-6$ is a factor of $2x^3+x^2+ax+b$,then $6a+13b=$

MediumAP EAMCET 2023

View Solution

The value of $\lambda$ such that the sum of the squares of the roots of the quadratic equation $x^2 + (3 - \lambda)x + 2 = \lambda$ has the least value is

DifficultJEE MAIN 2019

View Solution

If the roots of the equation $x^2 - (3k - 1)x + 2k^2 + 2k = 0$ are equal,then the value of $k$ will be .....

Difficult

View Solution

If the roots of the equation $x^2 + 2mx + m^2 - 2m + 6 = 0$ are equal,then the value of $m$ is:

Easy

View Solution

If for a positive integer $n$,the quadratic equation $x(x + 1) + (x + 1)(x + 2) + \dots + (x + n - 1)(x + n) = 10n$ has two consecutive integral solutions,then $n$ is equal to:

DifficultJEE MAIN 2017

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

What is the product of the real roots of the equation ${t^2}{x^2} + |x| + 9 = 0$?

Similar Questions

If $x^2+x-6$ is a factor of $2x^3+x^2+ax+b$,then $6a+13b=$

The value of $\lambda$ such that the sum of the squares of the roots of the quadratic equation $x^2 + (3 - \lambda)x + 2 = \lambda$ has the least value is

If the roots of the equation $x^2 - (3k - 1)x + 2k^2 + 2k = 0$ are equal,then the value of $k$ will be .....

If the roots of the equation $x^2 + 2mx + m^2 - 2m + 6 = 0$ are equal,then the value of $m$ is:

If for a positive integer $n$,the quadratic equation $x(x + 1) + (x + 1)(x + 2) + \dots + (x + n - 1)(x + n) = 10n$ has two consecutive integral solutions,then $n$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module