Real Root Polynomials and Real Root Preserving Transformations
Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial p with complex coefficients has a complex root. However, no analogous result holds for guaran...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/5585480 |
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| author | Suchada Pongprasert Kanyarat Chaengsisai Wuttichai Kaewleamthong Puttarawadee Sriphrom |
| author_facet | Suchada Pongprasert Kanyarat Chaengsisai Wuttichai Kaewleamthong Puttarawadee Sriphrom |
| author_sort | Suchada Pongprasert |
| collection | DOAJ |
| description | Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial p with complex coefficients has a complex root. However, no analogous result holds for guaranteeing that a real root exists to p if we restrict the coefficients to be real. Let n≥1 and Pn be the vector space of all polynomials of degree n or less with real coefficients. In this article, we give explicit forms of polynomials in Pn such that all of their roots are real. Furthermore, we present explicit forms of linear transformations on Pn which preserve real roots of polynomials in a certain subset of Pn. |
| format | Article |
| id | doaj-art-00ba8a30ef3f40b0934a04d4a36afbf8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-00ba8a30ef3f40b0934a04d4a36afbf82025-02-03T01:05:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252021-01-01202110.1155/2021/55854805585480Real Root Polynomials and Real Root Preserving TransformationsSuchada Pongprasert0Kanyarat Chaengsisai1Wuttichai Kaewleamthong2Puttarawadee Sriphrom3Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, ThailandDepartment of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, ThailandDepartment of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, ThailandDepartment of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, ThailandPolynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial p with complex coefficients has a complex root. However, no analogous result holds for guaranteeing that a real root exists to p if we restrict the coefficients to be real. Let n≥1 and Pn be the vector space of all polynomials of degree n or less with real coefficients. In this article, we give explicit forms of polynomials in Pn such that all of their roots are real. Furthermore, we present explicit forms of linear transformations on Pn which preserve real roots of polynomials in a certain subset of Pn.http://dx.doi.org/10.1155/2021/5585480 |
| spellingShingle | Suchada Pongprasert Kanyarat Chaengsisai Wuttichai Kaewleamthong Puttarawadee Sriphrom Real Root Polynomials and Real Root Preserving Transformations International Journal of Mathematics and Mathematical Sciences |
| title | Real Root Polynomials and Real Root Preserving Transformations |
| title_full | Real Root Polynomials and Real Root Preserving Transformations |
| title_fullStr | Real Root Polynomials and Real Root Preserving Transformations |
| title_full_unstemmed | Real Root Polynomials and Real Root Preserving Transformations |
| title_short | Real Root Polynomials and Real Root Preserving Transformations |
| title_sort | real root polynomials and real root preserving transformations |
| url | http://dx.doi.org/10.1155/2021/5585480 |
| work_keys_str_mv | AT suchadapongprasert realrootpolynomialsandrealrootpreservingtransformations AT kanyaratchaengsisai realrootpolynomialsandrealrootpreservingtransformations AT wuttichaikaewleamthong realrootpolynomialsandrealrootpreservingtransformations AT puttarawadeesriphrom realrootpolynomialsandrealrootpreservingtransformations |