Question

The polynomial P(z) = ^{3} +mz^{2} +nz - 8" alt="z^{3} +mz^{2} +nz - 8" align="absmiddle" class="latex-formula"> is divisible by (z+1+i), where z ∈C, m,n ∈R. Find the value of m and of n.

Answer 1

Answer:

m=-2   n=-6

Step-by-step explanation:

(z+1+i)(z+1-i)=z²+2z+1-(i²)=z²+2z+2

z³+mz²+nz-8=(z²+2z+2)(z-4)=z³-2z²-6z-8

m=-2

n=-6

If it's wrong, please delete it