(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

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(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

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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
$4$

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4-2.Quadratic Equations and Inequations

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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)$ $4$

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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:
$(1)$ $2$
$(2)$ $0$
$(3)$ $3$
$(4)$ $4$