(B) For the quadratic equation $x^2 + 4x \cos \theta + \cot \theta = 0$ to have equal roots,its discriminant $D$ must be zero.$D = b^2 - 4ac = (4 \cos

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

$\frac{\pi}{12}$ or $\frac{5 \pi}{12}$

(B) For the quadratic equation $x^2 + 4x \cos \theta + \cot \theta = 0$ to have equal roots,its discriminant $D$ must be zero.$D = b^2 - 4ac = (4 \cos \theta)^2 - 4(1)(\cot \theta) = 0$$16 \cos^2 \theta - 4 \cot \theta = 0$$4 \cos^2 \theta = \cot \theta$$4 \cos^2 \theta = \frac{\cos \theta}{\sin \theta}$Since $0 $4 \cos \theta \sin \theta = 1$$2 \sin 2 \theta = 1$$\sin 2 \theta = \frac{1}{2}$Since $0 Therefore,$\theta = \frac{\pi}{12}$ or $\theta = \frac{5 \pi}{12}$.

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

Difficult

Let $\theta$,$0 < \theta < \pi / 2$,be an angle such that the equation $x^2 + 4x \cos \theta + \cot \theta = 0$ has equal roots for $x$. Then $\theta$ in radians is

KVPY 2021 All KVPY

A
$\frac{\pi}{6}$ only
B
$\frac{\pi}{12}$ or $\frac{5 \pi}{12}$
C
$\frac{\pi}{6}$ or $\frac{5 \pi}{12}$
D
$\frac{\pi}{12}$ only

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

KVPY 2021 Paper All KVPY years →

If the roots of the quadratic equation $ax^2+bx+c=0$ are imaginary,then for all real values of $x$,the minimum value of the expression $3a^2x^2+6abx+2b^2$ is

EasyTS EAMCET 2020

View Solution

If $A$ and $G$ are arithmetic and geometric means and ${x^2} - 2Ax + {G^2} = 0$,then

Medium

View Solution

The equation $4^{(x^2 + 2)} - 9 \cdot 2^{(x^2 + 2)} + 8 = 0$ has the solution:

Difficult

View Solution

If the roots of the equation $x^2 - 8x + a^2 - 6a = 0$ are real,then what is the range of $a$?

Difficult

View Solution

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

Easy

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

Let $\theta$,$0 < \theta < \pi / 2$,be an angle such that the equation $x^2 + 4x \cos \theta + \cot \theta = 0$ has equal roots for $x$. Then $\theta$ in radians is

Similar Questions

If the roots of the quadratic equation $ax^2+bx+c=0$ are imaginary,then for all real values of $x$,the minimum value of the expression $3a^2x^2+6abx+2b^2$ is

If $A$ and $G$ are arithmetic and geometric means and ${x^2} - 2Ax + {G^2} = 0$,then

The equation $4^{(x^2 + 2)} - 9 \cdot 2^{(x^2 + 2)} + 8 = 0$ has the solution:

If the roots of the equation $x^2 - 8x + a^2 - 6a = 0$ are real,then what is the range of $a$?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module