(C) Let $y = \frac{x^2 + 14x + 9}{x^2 + 2x + 3}$.$y(x^2 + 2x + 3) = x^2 + 14x + 9$$x^2(y - 1) + 2x(y - 7) + (3y - 9) = 0$.Since $x$ is real,the discri

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

(C) Let $y = \frac{x^2 + 14x + 9}{x^2 + 2x + 3}$.$y(x^2 + 2x + 3) = x^2 + 14x + 9$$x^2(y - 1) + 2x(y - 7) + (3y - 9) = 0$.Since $x$ is real,the discriminant $D \geq 0$:$D = [2(y - 7)]^2 - 4(y - 1)(3y - 9) \geq 0$$4(y^2 - 14y + 49) - 4(3y^2 - 12y + 9) \geq 0$$y^2 - 14y + 49 - 3y^2 + 12y - 9 \geq 0$$-2y^2 - 2y + 40 \geq 0$$y^2 + y - 20 \leq 0$$(y + 5)(y - 4) \leq 0$.Thus,$y$ lies between $-5$ and $4$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Mix Examples-Quadratic Equations and Inequations

Difficult

If $x$ is real,then the value of the expression $\frac{x^2 + 14x + 9}{x^2 + 2x + 3}$ lies between

A
$5$ and $4$
B
$5$ and $-4$
C
$-5$ and $4$
D
None of these

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

Mix Examples-Quadratic Equations and Inequations

The number of pairs of real numbers $(x, y)$ such that $x = x^2 + y^2$ and $y = 2xy$ is:

KVPY 2009

View Solution

For what condition will the expression $a^2x^2 + bx + 1$ be positive for all $x \in R$?

Easy

View Solution

If $a, b, c$ are three positive numbers such that the maximum value of $abc^2$ is $1/64$,then:

Difficult

View Solution

If $\alpha, \beta$ are the roots of $x^2-a(x-1)+b=0$, then the value of $\frac{1}{\alpha^2-a \alpha}+\frac{1}{\beta^2-a \beta}+\frac{2}{a+b}$ is:

EasyWBJEE 2009

View Solution

The number of real solution$(s)$ of the equation $x^2+3x+2=\min \{|x-3|, |x+2|\}$ is:

DifficultJEE MAIN 2025

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 $x$ is real,then the value of the expression $\frac{x^2 + 14x + 9}{x^2 + 2x + 3}$ lies between

Similar Questions

The number of pairs of real numbers $(x, y)$ such that $x = x^2 + y^2$ and $y = 2xy$ is:

For what condition will the expression $a^2x^2 + bx + 1$ be positive for all $x \in R$?

If $a, b, c$ are three positive numbers such that the maximum value of $abc^2$ is $1/64$,then:

If $\alpha, \beta$ are the roots of $x^2-a(x-1)+b=0$, then the value of $\frac{1}{\alpha^2-a \alpha}+\frac{1}{\beta^2-a \beta}+\frac{2}{a+b}$ is:

The number of real solution$(s)$ of the equation $x^2+3x+2=\min \{|x-3|, |x+2|\}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module