2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165759Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex functions of higher order. Another application is some Hyers-Ulam-stability-type result.Functional AnalysisClassical Analysis and ODEs26A51, 26E25, 39B72, 54C65 (Primary); 26D07, 52A35 (Secondary)text