(B) Comparing the given equation $4x^{2} + 12x + 9 = 0$ with the standard form $ax^{2} + bx + c = 0$,we get:$a = 4, b = 12, c = 9$.The discriminant $D

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

(B) Comparing the given equation $4x^{2} + 12x + 9 = 0$ with the standard form $ax^{2} + bx + c = 0$,we get:$a = 4, b = 12, c = 9$.The discriminant $D$ is given by the formula $D = b^{2} - 4ac$.Substituting the values:$D = (12)^{2} - 4(4)(9)$$D = 144 - 144$$D = 0$.Since the discriminant $D = 0$,the quadratic equation has real and equal (repeated) roots.

Class 10 Mathematics Quadratic Equations Nature of Roots

Easy

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 12x + 9 = 0$.

A
Real and distinct roots
B
Real and equal roots
C
No real roots
D
Imaginary roots

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Quadratic Equations

Subtopic

Nature of Roots

If the value of the discriminant of a quadratic equation $6x^{2}-x-k=0$ is $25$,then $k = \ldots$

Easy

View Solution

Obtain the roots of the following quadratic equation by using the general formula for the solution: $2x^{2} - 2\sqrt{2}x + 1 = 0$.

Medium

View Solution

If the discriminant $D = 0$,then the roots of the quadratic equation $ax^2 + bx + c = 0$ are ..... .

Medium

View Solution

The value of the discriminant $D$ of the quadratic equation $x^{2} + 5x + 1 = 0$ is $\ldots \ldots \ldots \ldots .$

Easy

View Solution

Find whether the following equation has real roots. If real roots exist,find them.
$-2x^{2} + 3x + 2 = 0$

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

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 12x + 9 = 0$.

Similar Questions

If the value of the discriminant of a quadratic equation $6x^{2}-x-k=0$ is $25$,then $k = \ldots$

Obtain the roots of the following quadratic equation by using the general formula for the solution: $2x^{2} - 2\sqrt{2}x + 1 = 0$.

If the discriminant $D = 0$,then the roots of the quadratic equation $ax^2 + bx + c = 0$ are ..... .

The value of the discriminant $D$ of the quadratic equation $x^{2} + 5x + 1 = 0$ is $\ldots \ldots \ldots \ldots .$

Find whether the following equation has real roots. If real roots exist,find them.$-2x^{2} + 3x + 2 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Find whether the following equation has real roots. If real roots exist,find them.
$-2x^{2} + 3x + 2 = 0$