(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 2 Complex Numbers and Quadratic Equations: Quadratic Equations 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

2 Complex Numbers and Quadratic Equations: Quadratic Equations

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 →

If $p, q, r$ are in $A.P.$ and are positive,the roots of the quadratic equation $px^2 + qx + r = 0$ are all real for

DifficultIIT 1995

View Solution

$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

Difficult

View Solution

If a root of the equation $x^2 + px + 12 = 0$ is $4$,while the roots of the equation $x^2 + px + q = 0$ are equal,then the value of $q$ will be:

MediumAIEEE 2004

View Solution

Consider the equation $x^2+x-n = 0$,where $n \in N$ and $n \in [5, 100]$. The total number of different values of $n$ such that the given equation has integral roots is:

View Solution

Let $f(x)$ be a quadratic polynomial with $f(2)=10$ and $f(-2)=-2$. Then,the coefficient of $x$ in $f(x)$ is

MediumKVPY 2012

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

If $p, q, r$ are in $A.P.$ and are positive,the roots of the quadratic equation $px^2 + qx + r = 0$ are all real for

$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

If a root of the equation $x^2 + px + 12 = 0$ is $4$,while the roots of the equation $x^2 + px + q = 0$ are equal,then the value of $q$ will be:

Consider the equation $x^2+x-n = 0$,where $n \in N$ and $n \in [5, 100]$. The total number of different values of $n$ such that the given equation has integral roots is:

Let $f(x)$ be a quadratic polynomial with $f(2)=10$ and $f(-2)=-2$. Then,the coefficient of $x$ in $f(x)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module