Question

When the polynomial $5x^3+mx+n$ is divided by $x^2+x+1$ the remainder is $0$. The value of $(m+n)$ is equal to (where $m,n\in R$)

• A. $-3$
• B. $5$
• C. $-5$
• D. $15$

Answer 1

The correct option is C $-5$

$\omega$ and ${\omega }^2$ are roots of $x^2+x+1=0$
So they are roos of $5x^3+Mx+N=0$ also
third root must be 1 as sum of roots is zero and $1+\omega +{\omega }^2=0$
So the equation is $5(x-1)(x-\omega )(x-{\omega }^2=5(x^3-1)=0$
$⟹M=0N=-5$