(B) Let the two numbers be $x_1$ and $x_2$.The arithmetic mean is given by $\frac{x_1 + x_2}{2} = 9$,which implies $x_1 + x_2 = 18$.The geometric mean

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

(B) Let the two numbers be $x_1$ and $x_2$.The arithmetic mean is given by $\frac{x_1 + x_2}{2} = 9$,which implies $x_1 + x_2 = 18$.The geometric mean is given by $\sqrt{x_1 x_2} = 4$,which implies $x_1 x_2 = 4^2 = 16$.$A$ quadratic equation with roots $x_1$ and $x_2$ is given by $x^2 - (x_1 + x_2)x + (x_1 x_2) = 0$.Substituting the values,we get $x^2 - 18x + 16 = 0$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Relation between roots and coefficients

Easy

Let two numbers have an arithmetic mean of $9$ and a geometric mean of $4$. Then these numbers are the roots of the quadratic equation:

AIEEE 2004 All AIEEE

A
$x^2 - 18x - 16 = 0$
B
$x^2 - 18x + 16 = 0$
C
$x^2 + 18x - 16 = 0$
D
$x^2 + 18x + 16 = 0$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-2.Quadratic Equations and Inequations

Subtopic

Relation between roots and coefficients

Previous Year

AIEEE 2004 Paper All AIEEE years →

If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4+3x^3-6x^2+2x-4=0$,then find the equation having roots $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ and $\frac{1}{\delta}$.

MediumAP EAMCET 2020

View Solution

The cubic equation whose roots are the squares of the roots of $x^3-2x^2+10x-8=0$ is

DifficultTS EAMCET 2014

View Solution

If $A.M.$ and $G.M.$ of roots of a quadratic equation are $8$ and $5,$ respectively,then obtain the quadratic equation.

Easy

View Solution

Let $\alpha$ and $\beta$ be the roots of $x^{2}-6x-2=0$. If $a_{n}=\alpha^{n}-\beta^{n}$ for $n \geq 1$,then the value of $\frac{a_{10}-2a_{8}}{3a_{9}}$ is ..... .

DifficultJEE MAIN 2021

View Solution

If $\frac{\alpha}{\alpha+1}$ and $\frac{\beta}{\beta+1}$ are the roots of the quadratic equation $x^2+7x+3=0$,then the equation having roots $\alpha$ and $\beta$ is

EasyTS EAMCET 2021

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

Let two numbers have an arithmetic mean of $9$ and a geometric mean of $4$. Then these numbers are the roots of the quadratic equation:

Similar Questions

If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4+3x^3-6x^2+2x-4=0$,then find the equation having roots $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ and $\frac{1}{\delta}$.

The cubic equation whose roots are the squares of the roots of $x^3-2x^2+10x-8=0$ is

If $A.M.$ and $G.M.$ of roots of a quadratic equation are $8$ and $5,$ respectively,then obtain the quadratic equation.

Let $\alpha$ and $\beta$ be the roots of $x^{2}-6x-2=0$. If $a_{n}=\alpha^{n}-\beta^{n}$ for $n \geq 1$,then the value of $\frac{a_{10}-2a_{8}}{3a_{9}}$ is ..... .

If $\frac{\alpha}{\alpha+1}$ and $\frac{\beta}{\beta+1}$ are the roots of the quadratic equation $x^2+7x+3=0$,then the equation having roots $\alpha$ and $\beta$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module