(A) Given that $a, b, c$ are integers,the coefficients of the quadratic equation $ax^2 + bx + c = 0$ are rational.If one root of a quadratic equation

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

(A) Given that $a, b, c$ are integers,the coefficients of the quadratic equation $ax^2 + bx + c = 0$ are rational.If one root of a quadratic equation with rational coefficients is of the form $\alpha + \sqrt{\beta}$ (where $\sqrt{\beta}$ is an irrational surd),then the other root must be its conjugate,$\alpha - \sqrt{\beta}$.Here,one root is $3 + \sqrt{5}$.Therefore,the other root is $3 - \sqrt{5}$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

Medium

Let one root of $ax^2 + bx + c = 0$,where $a, b, c$ are integers,be $3 + \sqrt{5}$. Then the other root is:

A
$3 - \sqrt{5}$
B
$3$
C
$\sqrt{5}$
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

Solution of quadratic equations and Nature of roots

The value of $k$ for which the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots is:

Easy

View Solution

For the equation $x^2-5|x|-14=0$,which of the following is true?

EasyAP EAMCET 2021

View Solution

The equation whose roots are squares of the roots of $x^4-2 x^3+6 x-21=0$ is

EasyTS EAMCET 2021

View Solution

If $a$ and $b$ are odd integers, then the roots of the equation $2ax^2 + (2a + b)x + b = 0$, where $a \neq 0$, are

MediumWBJEE 2022

View Solution

The value of $k$ for which the equation $(k - 2)x^2 + 8x + k + 4 = 0$ has both roots real,distinct,and negative is

Easy

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 one root of $ax^2 + bx + c = 0$,where $a, b, c$ are integers,be $3 + \sqrt{5}$. Then the other root is:

Similar Questions

The value of $k$ for which the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots is:

For the equation $x^2-5|x|-14=0$,which of the following is true?

The equation whose roots are squares of the roots of $x^4-2 x^3+6 x-21=0$ is

If $a$ and $b$ are odd integers, then the roots of the equation $2ax^2 + (2a + b)x + b = 0$, where $a \neq 0$, are

The value of $k$ for which the equation $(k - 2)x^2 + 8x + k + 4 = 0$ has both roots real,distinct,and negative is

Vedclass Test Series

Exam Paper Generator

Online Exam Module