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Operations research, linear programming, control theory, systems theory, optimal control, game theory

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Some calculations with polynomials in the proof of the Routh-Hurwitz test

In an article on the Routh-Hurwitz test, I couldn't see why the following result is true: Let $$p(s)=a_ns^n+a_{n-1}s^{n-1}+\dots+a_{1}s+a_0$$ and $$ \eta_{*} = \frac{a_n}{a_{n-1}}$$ $$g_{\eta}(s):=p( …