(D) Let $y = \frac{x^2-3x+4}{x^2+3x+4}$.$y(x^2+3x+4) = x^2-3x+4$$yx^2 + 3yx + 4y = x^2 - 3x + 4$$x^2(y-1) + x(3y+3) + (4y-4) = 0$.Since $x$ is real, t

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

(D) Let $y = \frac{x^2-3x+4}{x^2+3x+4}$.$y(x^2+3x+4) = x^2-3x+4$$yx^2 + 3yx + 4y = x^2 - 3x + 4$$x^2(y-1) + x(3y+3) + (4y-4) = 0$.Since $x$ is real, the discriminant $D \geq 0$.$D = (3y+3)^2 - 4(y-1)(4y-4) \geq 0$$9(y+1)^2 - 16(y-1)^2 \geq 0$$9(y^2+2y+1) - 16(y^2-2y+1) \geq 0$$9y^2 + 18y + 9 - 16y^2 + 32y - 16 \geq 0$$-7y^2 + 50y - 7 \geq 0$$7y^2 - 50y + 7 \leq 0$$(7y-1)(y-7) \leq 0$.Thus, the interval is $[\frac{1}{7}, 7]$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Mix Examples-Quadratic Equations and Inequations

Medium

If $x$ is real, then the value of $\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval

TS EAMCET 2011 All TS EAMCET

AP EAMCET 2011 All AP EAMCET

A
$[\frac{1}{3}, 3]$
B
$[\frac{1}{5}, 5]$
C
$[\frac{1}{6}, 6]$
D
$[\frac{1}{7}, 7]$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-2.Quadratic Equations and Inequations

Subtopic

Mix Examples-Quadratic Equations and Inequations

Previous Year

TS EAMCET 2011 Paper All TS EAMCET years →

Previous Year

AP EAMCET 2011 Paper All AP EAMCET years →

The sum of all integral values of $k$ $(k \neq 0)$ for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$ in $x$ has no real roots,is ..... .

DifficultJEE MAIN 2021

View Solution

For real values of $x$,the range of $\frac{x^2+2x+1}{x^2+2x-1}$ is

MediumAP EAMCET 2015

View Solution

If $ax + by = 1$,where $a, b, x$ and $y$ are integers,then which one of the following is not true?

EasyKCET 2009

View Solution

The number of integral values of $a$ for which $x^2 - (a - 1)x + 3 = 0$ has both roots positive and $x^2 + 3x + 6 - a = 0$ has both roots negative is

View Solution

Let $a, b, c, d \in R^+$ such that $256abcd \geq (a+b+c+d)^4$ and $3a + b + 2c + 5d = 11$. Then $a^3 + b + c^2 + 5d$ is equal to:

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 $\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval

Similar Questions

The sum of all integral values of $k$ $(k \neq 0)$ for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$ in $x$ has no real roots,is ..... .

For real values of $x$,the range of $\frac{x^2+2x+1}{x^2+2x-1}$ is

If $ax + by = 1$,where $a, b, x$ and $y$ are integers,then which one of the following is not true?

The number of integral values of $a$ for which $x^2 - (a - 1)x + 3 = 0$ has both roots positive and $x^2 + 3x + 6 - a = 0$ has both roots negative is

Let $a, b, c, d \in R^+$ such that $256abcd \geq (a+b+c+d)^4$ and $3a + b + 2c + 5d = 11$. Then $a^3 + b + c^2 + 5d$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module