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Euclidean-Cardano and Cantor-Cardano cubic polynomials
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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.
Springer Science and Business Media LLC
Title: Euclidean-Cardano and Cantor-Cardano cubic polynomials
Description:
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.
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