The aim of this paper is to prove that the polynomial \(P(Y)=Y^n+A_{n-1}Y^{n-1}+\cdots +A_{n-k+1}Y^{n-k+1}+A_{n-k}Y^{n-k}+ \cdots + A_1 Y+ A_0\) with \(A_0 \ne 0\) , \(|A_{n-k} |> \underset{i \ne n-k}{|A_i|}\) , \(\deg A_{n-k} > k \ \underset{1 \le i \le k-1}{\max \deg A_{n-i}}\) , \(k \not | \deg A_{n-k},\) and \( n \ge k+1\) , has no root in \(\mathbb {F}_q((X^{-1}))\) with modulus strictly greater than 1. Moreover P is irreducible over \(\mathbb {F}_q[X]\) . We provide the generalization of a previous result extended given by Ben Nasr and Kthiri.
