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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
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: PDF
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
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  Data: Geometrical Solutions of Some Quadratic Equations with Non-Real Roots
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  Data: <searchLink fieldCode="SO" term="%22International+Journal+of+Mathematical+Education+in+Science+and+Technology%22"><i>International Journal of Mathematical Education in Science and Technology</i></searchLink>. Jan 2002 33(1):150-156.
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  Data: 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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