Geometrical Solutions of Some Quadratic Equations with Non-Real Roots
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| Title: | Geometrical Solutions of Some Quadratic Equations with Non-Real Roots |
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| Language: | English |
| Authors: | Pathak, H. K., Grewal, A. S. |
| Source: | International Journal of Mathematical Education in Science and Technology. Jan 2002 33(1):150-156. |
| Availability: | Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html |
| Peer Reviewed: | Y |
| Physical Description: | |
| Page Count: | 7 |
| Publication Date: | 2002 |
| Document Type: | Journal Articles Reports - Descriptive |
| Descriptors: | Numbers, Algebra, Mathematics Activities, Geometry, Equations (Mathematics), Problem Solving, Mathematics Instruction |
| DOI: | 10.1080/00207390210210 |
| ISSN: | 0020-739X |
| Abstract: | This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when a, b, c [is a member of] R, the set of real numbers, are presented. Case II deals with the geometrical solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when b [is a member of] R, the set of real numbers; and a, c [is a member of] C, the set of complex numbers. Finally, the solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when a, c [is a member of] R, the set of real numbers, and b [is a member of] C, the set of complex numbers, are presented in case III. (Contains 3 figures.) |
| Abstractor: | Author |
| Number of References: | 1 |
| Entry Date: | 2007 |
| Accession Number: | EJ770349 |
| Database: | ERIC |
| Abstract: | This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when a, b, c [is a member of] R, the set of real numbers, are presented. Case II deals with the geometrical solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when b [is a member of] R, the set of real numbers; and a, c [is a member of] C, the set of complex numbers. Finally, the solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, when a, c [is a member of] R, the set of real numbers, and b [is a member of] C, the set of complex numbers, are presented in case III. (Contains 3 figures.) |
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| ISSN: | 0020-739X |
| DOI: | 10.1080/00207390210210 |
