Consider the complex poynomial $$P(z)=z^{n+1}-z^n+\epsilon c$$ with positive integer $n$, real $\epsilon>0$ and complex $c$ with $Re(c)>0$. I am interested in finding explicit upper bounds on $\epsilon$ such that all roots lie within the unit circle.
An answer for the special case $n=1$ has been given in my earlier question by @dxiv.