2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125609We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the in- and circumradius of the convex body. We show that the roots of 1-tangential bodies fulfill the conjecture, but we also present convex bodies violating each of the conjectured properties.Metric Geometry52A20 (Primary); 52A39, 30C15 (Secondary)text