Consider the polynomial $$f(x)=p_0x^n+p_1x^{n-1}+...+p_{n-1}x+p_n,~p_i \in \mathbb C.$$ Particularly, in the case of absolute stability of a multi-step numerical method, how can we find out the region $R$ in $\mathbb C$ such that $p_i \in R$ ensures that $|t| \leq 1$ for any root $t$ of $f$.
For instance, suppose that we have a polynomial like $$f(t)=\frac{8081}{1781} t^{3}-\frac{12627}{1781} t^{3} H-\frac{8745}{1781} t^{2}+\frac{7992}{1781} t^{3} H^{2}-\frac{9738}{1781} t^{2} H+\frac{1}{1781}$$ Any easy technique is available to find the region $R$ such that $H \in R$ ensures that $|t| \leq 1$ for any root $t$ of $f$?
Is it possible to find in mathematica or maple?