SIMPLE FORMULAE FOR THE EVALUATION OF ALL THE EXACT ROOTS (REAL AND COMPLEX) OF THE GENERAL CUBIC

Authors

  • AJ Anyaegunam Department of Civil Engineering, University of Nigeria, Nsukka

DOI:

https://doi.org/10.4314/njt.271.520

Keywords:

General cubic, trigonometric, hyperbolic, simple formulae, complex roots

Abstract

Simplified explicit formulae for the evaluation of the exact roots of the general cubic equation ax3 + bx2 + cx + d  =  0 have been formulated and presented. The explicit hyperbolic expressions for the complex roots have been developed for the first time in history thereby enabling the establishment of harmony in the solution of cubic equations. Also, four alternative expressions for the only real root of the cubic have also been given for those cases when the discriminant is positive.

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Section

Research papers of General Interest

How to Cite

SIMPLE FORMULAE FOR THE EVALUATION OF ALL THE EXACT ROOTS (REAL AND COMPLEX) OF THE GENERAL CUBIC. (2008). Nigerian Journal of Technology, 27(1), 48-53. https://doi.org/10.4314/njt.271.520