(A) Given the quadratic equation $x^2 + px + q = 0$ with rational coefficients,if one root is $2 + \sqrt{3}$,the other root must be its conjugate,$2 -

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

(A) Given the quadratic equation $x^2 + px + q = 0$ with rational coefficients,if one root is $2 + \sqrt{3}$,the other root must be its conjugate,$2 - \sqrt{3}$.Sum of roots $= -p = (2 + \sqrt{3}) + (2 - \sqrt{3}) = 4$,which implies $p = -4$.Product of roots $= q = (2 + \sqrt{3})(2 - \sqrt{3}) = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1$.Therefore,the values are $(p, q) = (-4, 1)$.

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

Easy

If one root of the equation $x^2 + px + q = 0$ is $2 + \sqrt{3}$,then the values of $p$ and $q$ are:

A
$-4, 1$
B
$4, -1$
C
$2, \sqrt{3}$
D
$-2, -\sqrt{3}$

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

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

DifficultAP EAMCET 2004

View Solution

If both roots of the equation $x^2 + \lambda x + \mu = 0$ are equal and one root of the equation $x^2 + \lambda x - 12 = 0$ is $2$,then $(\lambda, \mu) = \dots$

Medium

View Solution

If the two roots of the equation $(a - 1)(x^4 + x^2 + 1) + (a + 1)(x^2 + x + 1)^2 = 0$ are real and distinct,then the set of all values of $a$ is

DifficultJEE MAIN 2015

View Solution

$A$ 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

If $\alpha, \beta$ are the irrational roots of the equation $3p^2x^3 + px^2 + qx + 3 = 0$ when $p = 1$ and $q = -7$,then $|\alpha - \beta| = $

MediumTS EAMCET 2022

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 one root of the equation $x^2 + px + q = 0$ is $2 + \sqrt{3}$,then the values of $p$ and $q$ are:

Similar Questions

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

If both roots of the equation $x^2 + \lambda x + \mu = 0$ are equal and one root of the equation $x^2 + \lambda x - 12 = 0$ is $2$,then $(\lambda, \mu) = \dots$

If the two roots of the equation $(a - 1)(x^4 + x^2 + 1) + (a + 1)(x^2 + x + 1)^2 = 0$ are real and distinct,then the set of all values of $a$ is

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

If $\alpha, \beta$ are the irrational roots of the equation $3p^2x^3 + px^2 + qx + 3 = 0$ when $p = 1$ and $q = -7$,then $|\alpha - \beta| = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module