Abstract
It is a well known fact that there exist irreducible polynomials P(X) over \(\mathbb {Z}\) that are not p-Eisenstanian for any prime number p at a first glance but, after a linear transformation Eisenstein criterion could be applied to obtain their irreducibility. One of the main purpose of this paper is to give families of irreducible quartics that are not of this kind. We also study the problem of the root separation for quartic polynomials.
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