(A) Given $a + b + c + d = 2$. Let $x = a + b$ and $y = c + d$. Then $x + y = 2$ and $M = xy$.By the Arithmetic Mean-Geometric Mean inequality $(AM \g

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

(A) Given $a + b + c + d = 2$. Let $x = a + b$ and $y = c + d$. Then $x + y = 2$ and $M = xy$.By the Arithmetic Mean-Geometric Mean inequality $(AM \ge GM)$,we have $\frac{x + y}{2} \ge \sqrt{xy}$.Substituting the values,$\frac{2}{2} \ge \sqrt{M}$,which implies $1 \ge \sqrt{M}$,or $M \le 1$.Since $a, b, c, d$ are positive real numbers,$x > 0$ and $y > 0$,so $M = xy > 0$.Thus,the relation is $0 < M \le 1$.

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

Medium

If $a, b, c, d$ are positive real numbers such that $a + b + c + d = 2$,then $M = (a + b)(c + d)$ satisfies the relation:

IIT 2000 All IIT

A
$0 < M \le 1$
B
$1 \le M \le 2$
C
$2 \le M \le 3$
D
$3 \le M \le 4$

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

IIT 2000 Paper All IIT years →

$A$ 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

The difference of the irrational roots of the equation $x^5-5x^4+9x^3-9x^2+5x-1=0$ is

DifficultAP EAMCET 2017

View Solution

The number of pairs $(a, b)$ of real numbers such that whenever $\alpha$ is a root of the equation $x^{2}+ax+b=0$,$\alpha^{2}-2$ is also a root of this equation,is:

DifficultJEE MAIN 2021

View Solution

If $2+\sqrt{3}$ is a root of the equation $f(x)=x^4+2x^3-16x^2-22x+7=0$,then which one of the following is not a root of $f(x)=0$?

EasyTS EAMCET 2020

View Solution

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

DifficultTS EAMCET 2002

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 $a, b, c, d$ are positive real numbers such that $a + b + c + d = 2$,then $M = (a + b)(c + d)$ satisfies the relation:

Similar Questions

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

The difference of the irrational roots of the equation $x^5-5x^4+9x^3-9x^2+5x-1=0$ is

The number of pairs $(a, b)$ of real numbers such that whenever $\alpha$ is a root of the equation $x^{2}+ax+b=0$,$\alpha^{2}-2$ is also a root of this equation,is:

If $2+\sqrt{3}$ is a root of the equation $f(x)=x^4+2x^3-16x^2-22x+7=0$,then which one of the following is not a root of $f(x)=0$?

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

Vedclass Test Series

Exam Paper Generator

Online Exam Module