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<p>The aim of this paper is to introduce and study two classes of cubic real polynomials <i>P</i> 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 <i>P</i> 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.</p>

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Euclidean-Cardano and Cantor-Cardano cubic polynomials

  • 期刊论文

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  • 发表日期：

    2026年4月6日

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  • Mircea Crasmareanu

摘要

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.