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If 5x^(3) +Mx+ N, M,N in R is divisib...

If `5x^(3) +Mx+ N, M,N in R` is divisible by `x^(2) + x+1`, then the value of `M +N ` is

A

5

B

4

C

`-4`

D

`-5`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x)=5x^(2)+Mx+N`.
Also, `x^(2)+x+1=(x-omega)(x-omega^(2))`
It is given that `f(x)` is divisible by `x^(2)+x+1`.
`therefore f(omega)=5+Momega+N=0`
and `f(omega^(2))=5+Momega^(2)+N=0`
So, `M =0 and N=-5`
`therefore M+N =-5`
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