The Journal of Pedagogical University of Cracow

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Annales Uni. P. Cr. St. M.

<abstract>
<title style='display:none'>Abstract</title>
Since <italic>Geronimo Cardano</italic>, algebraic equations of degree 4 have been solved analytically. Frequently, the solution algorithm is given in its entirety. We discovered two algorithms that lead to the same <italic>resolvente</italic>, each with two solutions; therefore, six formal solutions appear to solve an algebraic equation of degree four. Given that a square was utilized to derive the solution in both instances, it is critical to verify each solution. This check reveals that the four Cardanic solutions are the only four solutions to an algebraic equation of degree four. This demonstrates that <italic>Carl Friedrich Gauss</italic>’ (1799) <italic>fundamental theorem of algebra</italic> is not simple, despite the fact that it is a fundamental theorem. This seems to be a novel insight.
</abstract>

Abstract

Keywords

<article-title>Solution to algebraic equations of degree 4 and the fundamental theorem of algebra by Carl Friedrich Gauss</article-title>

Solution to algebraic equations of degree 4 and the fundamental theorem of algebra by Carl Friedrich Gauss

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica is covered by the following services: <UL> <LI>Arianta </LI> <LI>Baidu Scholar </LI> <LI>CNKI Scholar (China National Knowledge Infrastructure) </LI> <LI>CNPIEC - cnpLINKer </LI> <LI>Dimensions </LI> <LI>DOAJ (Directory of Open Access Journals) </LI> <LI>EBSCO </LI> <LI>ExLibris </LI> <LI>Google Scholar </LI> <LI>Index Copernicus </LI> <LI>Japan Science and Technology Agency (JST) </LI> <LI>J-Gate </LI> <LI>JournalGuide </LI> <LI>JournalTOCs </LI> <LI>KESLI-NDSL (Korean National Discovery for Science Leaders) </LI> <LI>Mathematical Reviews (MathSciNet) </LI> <LI>MyScienceWork </LI> <LI>Naver Academic </LI> <LI>Naviga (Softweco) </LI> <LI>QOAM (Quality Open Access Market) </LI> <LI>ReadCube </LI> <LI>SCILIT </LI> <LI>Semantic Scholar </LI> <LI>Sherpa/RoMEO </LI> <LI>TDNet </LI> <LI>The Polish Digital Mathematical Library (DML-PL) </LI> <LI>Ulrich's Periodicals Directory/ulrichsweb </LI> <LI>WanFang Data </LI> <LI>Web of Science - Emerging Sources Citation Index </LI> <LI>WorldCat (OCLC) </LI> <LI>X-MOL </LI> <LI>zbMATH Open </LI></UL>

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica ist in den folgenden Services indiziert: <UL> <LI>Arianta </LI> <LI>Baidu Scholar </LI> <LI>CNKI Scholar (China National Knowledge Infrastructure) </LI> <LI>CNPIEC - cnpLINKer </LI> <LI>Dimensions </LI> <LI>DOAJ (Directory of Open Access Journals) </LI> <LI>EBSCO </LI> <LI>ExLibris </LI> <LI>Google Scholar </LI> <LI>Index Copernicus </LI> <LI>Japan Science and Technology Agency (JST) </LI> <LI>J-Gate </LI> <LI>JournalGuide </LI> <LI>JournalTOCs </LI> <LI>KESLI-NDSL (Korean National Discovery for Science Leaders) </LI> <LI>Mathematical Reviews (MathSciNet) </LI> <LI>MyScienceWork </LI> <LI>Naver Academic </LI> <LI>Naviga (Softweco) </LI> <LI>QOAM (Quality Open Access Market) </LI> <LI>ReadCube </LI> <LI>SCILIT </LI> <LI>Semantic Scholar </LI> <LI>Sherpa/RoMEO </LI> <LI>TDNet </LI> <LI>The Polish Digital Mathematical Library (DML-PL) </LI> <LI>Ulrich's Periodicals Directory/ulrichsweb </LI> <LI>WanFang Data </LI> <LI>Web of Science - Emerging Sources Citation Index </LI> <LI>WorldCat (OCLC) </LI> <LI>X-MOL </LI> <LI>zbMATH Open </LI></UL>

Editor-in-Chief Paweł Wójcik, Pedagogical University of Krakow, Poland Editors and Editorial Advisory Board Wojciech Chachólski, Royal Institute of Technology, KTH, Sweden Márton Elekes, Hungarian Academy of Sciences, Hungary Beata Gryszka, Pedagogical University of Krakow, Poland (secretary) Karol Gryszka, Pedagogical University of Krakow, Poland (secretary) Giovanna Ilardi, Università degli studi di Napoli ’’Federico II”, Italy Alex Küronya, Budapest University of Technology and Economics, Hungary Mohammad Sal Moslehian, Ferdowsi University of Mashhad, Iran Zsolt Páles, University of Debrecen, Hungary Tomasz Szemberg, PedagoPedagogical University of Krakow, Poland Justyna Szpond, Pedagogical University of Krakow, Poland Behrouz Taji, Albert Ludwigs University of Freiburg, Germany Technical Editors Paweł Pasteczka, Pedagogical University of Krakow, Poland Paweł Solarz, Pedagogical University of Krakow, Poland Contact <A href="mailto:studmath@up.krakow.pl">studmath@up.krakow.pl</A> Publisher De Gruyter Poland Bogumiła Zuga 32A Str. 01-811 Warsaw, Poland T: +48 22 701 50 15

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<DIV align=left> Scope and AIM Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica (AUPC SM) publishes high quality original papers on new methods and results that hold prospect for substantial progress in mathematics. Our scope focuses on the following branches of the contemporary mathematics, namely analysis, algebra, combinatorics, geometry, number theory, and topology. However, we can also consider for publication high quality papers from other subjects that could potentially have a significant impact on the development of mathematics. We also accept well-written survey and expository papers. Short announcements on future results are not accepted. The Editorial Board expects high standards of submissions; we look for articles that inform, stimulate, challenge, or even enlighten. Novelty, clarity of exposition, and broad appeal lies in the priority of the journal. Appropriate figures, tables, and diagrams are strongly encouraged. Quick and fair processing of all submissions is our priority. All submitted papers undergo a refereeing procedure by an international board whose members represent a wide spectrum of research interests. Publication in Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica is free of charge (Diamond Open Access -- free to read and free to publish). Volumes I-VII appeared as Annales Academiae Paedagogicae Cracoviensis Studia Mathematica. Archiving Sciendo archives the contents of this journal in <A href="https://www.portico.org/">Portico</A> - digital long-term preservation service of scholarly books, journals and collections. Plagiarism Policy The editorial board is participating in a growing community of <A href="https://www.crossref.org/services/similarity-check/">Similarity Check System's</A> users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. Target Group - researchers in all branches of pure mathematics</DIV>

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Solution to algebraic equations of degree 4 and the fundamental theorem of algebra by Carl Friedrich Gauss

Norbert Südland,
Norbert Südland,
Jörg Volkmann and
Jörg Volkmann and
Dinesh Kumar
Dinesh Kumar

Published Online: 08 Dec 2022

Volume & Issue: Volume 21 (2022) - Issue 1 (January 2022)

Page range: 57 - 70

Received: 05 Apr 2022

Accepted: 20 Sep 2022

Journal & Issue Details

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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References

Recent Articles

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Solution to algebraic equations of degree 4 and the fundamental theorem of algebra by Carl Friedrich Gauss

Norbert Südland,Norbert Südland,Jörg Volkmann andJörg Volkmann andDinesh KumarDinesh Kumar

Published Online: 08 Dec 2022

Volume & Issue: Volume 21 (2022) - Issue 1 (January 2022)

Page range: 57 - 70

Received: 05 Apr 2022

Accepted: 20 Sep 2022

Journal & Issue Details

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

PDF Preview

References

Recent Articles

Norbert Südland,
Norbert Südland,
Jörg Volkmann and
Jörg Volkmann and
Dinesh Kumar
Dinesh Kumar