(B) Given that $x^4+x^2+1$ is divisible by both $x^2+mx+1$ and $x^2+nx+1$.Since the polynomial is of degree $4$ and the divisors are of degree $2$,we

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

(B) Given that $x^4+x^2+1$ is divisible by both $x^2+mx+1$ and $x^2+nx+1$.Since the polynomial is of degree $4$ and the divisors are of degree $2$,we can write:$x^4+x^2+1 = (x^2+mx+1)(x^2+nx+1)$Expanding the right side:$x^4 + nx^3 + x^2 + mx^3 + mnx^2 + mx + x^2 + nx + 1$$= x^4 + (m+n)x^3 + (mn+2)x^2 + (m+n)x + 1$Comparing the coefficients of $x^3$ on both sides,we get:$m+n = 0$

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

Medium

If a polynomial $x^4+x^2+1$ is divisible by $x^2+mx+1$ and $x^2+nx+1$,then $m+n$ is equal to:
$(1)$ $2$
$(2)$ $0$
$(3)$ $3$
$(4)$ $4$

AP EAMCET 2020 All AP EAMCET

A
$2$
B
$0$
C
$3$
D
$4$

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

AP EAMCET 2020 Paper All AP EAMCET years →

If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \text{to } \infty}}}$,then

Medium

View Solution

If the equation $x^2 - m(2x - 8) - 15 = 0$ has equal roots,then $m = ......$

Easy

View Solution

If the roots of the equations $ax^2 + 2bx + c = 0$ and $bx^2 - 2\sqrt{ac}x + b = 0$ are real,then:

Easy

View Solution

If the expression $x^3+3x^2-9x+\lambda$ is of the form $(x-\alpha)^2(x-\beta)$,then the values of $\lambda$ are

MediumTS EAMCET 2023

View Solution

For how many values of $k$ is the equation $(1 + 2k)x^2 + (1 - 2k)x + (1 - 2k) = 0$ a perfect square?

Medium

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 polynomial $x^4+x^2+1$ is divisible by $x^2+mx+1$ and $x^2+nx+1$,then $m+n$ is equal to:$(1)$ $2$$(2)$ $0$$(3)$ $3$$(4)$ $4$

Similar Questions

If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \text{to } \infty}}}$,then

If the equation $x^2 - m(2x - 8) - 15 = 0$ has equal roots,then $m = ......$

If the roots of the equations $ax^2 + 2bx + c = 0$ and $bx^2 - 2\sqrt{ac}x + b = 0$ are real,then:

If the expression $x^3+3x^2-9x+\lambda$ is of the form $(x-\alpha)^2(x-\beta)$,then the values of $\lambda$ are

For how many values of $k$ is the equation $(1 + 2k)x^2 + (1 - 2k)x + (1 - 2k) = 0$ a perfect square?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If a polynomial $x^4+x^2+1$ is divisible by $x^2+mx+1$ and $x^2+nx+1$,then $m+n$ is equal to:
$(1)$ $2$
$(2)$ $0$
$(3)$ $3$
$(4)$ $4$