Euclidean-Cardano and Cantor-Cardano cubic polynomials

Abstract The aim of this paper is to introduce and study two classes of cubic real polynomials P having the same Euclidean norm as their Cardano resolvent respectively having the square of the Euclidean norm equal to the height of the Cardano resolvent. The polynomial P is giving in its reduced form which means without the cubic term. We find three one-parameter families of polynomials in the first class. For the second class of polynomials we discuss some cases.