When a polynomial has exactly one positive root and no roots in \((-1,0)\) (Q917603)

The author describes necessary and sufficient conditions for a polynomial with real coefficients to have exactly one positive root, \(m\) null roots, and all the other roots less than \(-1\). This result is obtained by a careful study of a modified Pratt tableau [\textit{J. W. Pratt}, Am. Math. Mon. 86, No. 8, 630--647 (1979; Zbl 0425.26006)]. Among many technical results we mention the description of necessary and sufficient conditions for a polynomial to have real roots outside \([-1,0]\). The main results are algorithmic.