My problem is the following:
Let $k$ be a strictly positive integer and let's look at a polynomial $$X^k - c_0 X^{k-1} - \ldots - c_{k-1}$$ that we suppose irreductible over $\mathbb{Z}$, where $c_0, \ldots , c_{k-1}$ are integers. Let's denote $\alpha$ the dominant root of the polynomial and suppose that $\alpha \in \mathbb{R}$ and $\alpha > 0$.
I already know that $\alpha \leq 1 + \max_{i \in \{0 , \ldots , k-1\}} \vert c_i \vert$ (Descartes).
What are the conditions on $c_0 , \ldots , c_{k-1}$ to have $\alpha \geq c_{k-1}$?
Thanks for any answer.