Problem:

Is it possible to determine the real constant a so that

$\displaystyle z=2+i$

is a root for the equation

$\displaystyle z^3+az^2+13z-10=0$

I started out like so that if p(b)=0, where p(z) is a polynomial of a degree n,

then p(z)=(z-b)*f(z) where f(z) is a polynomial of a degree n-1

meaning that

$\displaystyle z^3+az^3+13z-10=(z-(2+1))(z^2+dz+e)$

but apparently that was wrong..

Sorry for all the questions, but I have an exam coming up this monday