Solution to algebraic equations of degree~4 and the fundamental theorem of algebra by Carl Friedrich Gauss
| Autor: | Norbert Südland, Jörg Volkmann, Dinesh Kumar |
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| Jazyk: | German<br />English<br />French |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, Vol 21, Pp 57-70 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2081-545X 2300-133X |
| Popis: | Since Geronimo Cardano, 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 resolvente, 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 Carl Friedrich Gauss' (1799) fundamental theorem of algebra is not simple, despite the fact that it is a fundamental theorem. This seems to be a novel insight. |
| Databáze: | Directory of Open Access Journals |
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