Let $\alpha$ be a root of a polynomial $a_nx^n + \ldots + a_1x$ with integral coefficients.
I would like to determine $\varepsilon > 0$ depending on $a_1, \ldots, a_n$ so that $|\alpha| < \varepsilon$ implies $\alpha = 0$.
Is it possible to give a "formula" for such an $\varepsilon$ without refering to the complete list of roots?