(C) Given equation: $(\cos p-1) x^2+(\cos p) x+\sin p=0$. Since the roots are real,the discriminant $\Delta \geq 0$. $\Delta = b^2 - 4ac = (\cos p)^2

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

(C) Given equation: $(\cos p-1) x^2+(\cos p) x+\sin p=0$. Since the roots are real,the discriminant $\Delta \geq 0$. $\Delta = b^2 - 4ac = (\cos p)^2 - 4(\cos p - 1)(\sin p) \geq 0$. $\cos^2 p - 4\sin p \cos p + 4\sin p \geq 0$. For the quadratic equation to exist,the coefficient of $x^2$ must be non-zero: $\cos p - 1 \neq 0 \Rightarrow \cos p \neq 1$. Since $\cos^2 p \geq 0$ and $(\cos p - 1) 0$. Thus,$p \in (0, \pi)$. Hence,option $C$ is correct.

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

Easy

If the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

AP EAMCET 2020 All AP EAMCET

IIT 1990 All IIT

A
$p \in(-\pi, 0)$
B
$p \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
C
$p \in(0, \pi)$
D
$p \in(0, 2\pi)$

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

AP EAMCET 2020 Paper All AP EAMCET years →

Previous Year

IIT 1990 Paper All IIT years →

Consider a quadratic equation $ax^2 + 2bx + c = 0$ where $a, b, c$ are positive real numbers. If the equation has no real root, then which of the following is true?

DifficultWBJEE 2023

View Solution

If the difference between the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ is the same,then $b + c = \dots$

Difficult

View Solution

The roots of the equation $3^{2x} - 10 \cdot 3^x + 9 = 0$ are

Easy

View Solution

If $AM$ and $GM$ of roots of a quadratic equation are $5$ and $4$,respectively,then the quadratic equation is

EasyKCET 2024

View Solution

The product and sum of the roots of the equation $|x|^2 - 5|x| - 24 = 0$ are respectively:

EasyAP EAMCET 2016

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 the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

Similar Questions

Consider a quadratic equation $ax^2 + 2bx + c = 0$ where $a, b, c$ are positive real numbers. If the equation has no real root, then which of the following is true?

If the difference between the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ is the same,then $b + c = \dots$

The roots of the equation $3^{2x} - 10 \cdot 3^x + 9 = 0$ are

If $AM$ and $GM$ of roots of a quadratic equation are $5$ and $4$,respectively,then the quadratic equation is

The product and sum of the roots of the equation $|x|^2 - 5|x| - 24 = 0$ are respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module