I would please like some help with solving the following equation:
$$z^4 - 2z^3 + 9z^2 - 14z + 14 = 0$$
All I know about the equation is that there is a root with the real part of $1$.
My approach has been to factor out the root: $1 + yi$ and divide the equation with it. The following calculations (using the division algorithm) is quite cumbersome, and I wonder if there is any better way of doing this?
Thank you kindly for your help!