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.
Mircea Crasmareanu (Mon,) studied this question.
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