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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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 y
Jörg Volkmann y
Dinesh Kumar
Dinesh Kumar

Publicado en línea: 08 Dec 2022

Volumen & Edición: Volumen 21 (2022) - Edición 1 (January 2022)

Páginas: 57 - 70

Recibido: 05 Apr 2022

Aceptado: 20 Sep 2022

Detalles de publicación y publicación

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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Artículos Recientes

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 yJörg Volkmann yDinesh KumarDinesh Kumar

Publicado en línea: 08 Dec 2022

Volumen & Edición: Volumen 21 (2022) - Edición 1 (January 2022)

Páginas: 57 - 70

Recibido: 05 Apr 2022

Aceptado: 20 Sep 2022

Detalles de publicación y publicación

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Vista previa del PDF

Referencias

Artículos Recientes

Norbert Südland,
Norbert Südland,
Jörg Volkmann y
Jörg Volkmann y
Dinesh Kumar
Dinesh Kumar