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The geometry of the discriminant of a polynomial

Published online by Cambridge University Press:  01 August 2016

R. W. D. Nickalls  and
R. H. Dye
R. W. D. Nickalls
Affiliation:
Department of Anaesthesia, City Hospital NHS Trust, Nottingham NG7 2UH, dick.nickalls@nottingham.ac.uk
R. H. Dye
Affiliation:
Department of Mathematics and Statistics, University of Newcastle NE1 7RH
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Extract

Everyone knows that the condition for the quadratic to have two equal roots, i.e. to have a repeated root, is that its discriminant should be zero. We should remark, at the outset, that we are concerned only with ordinary polynomials whose coefficients are complex numbers. Indeed, little is lost if a reader assumes that all our polynomials are real, i.e. have real numbers for all their coefficients, though their complex roots must be considered as well as their real ones.

Type
Articles
Information
The Mathematical Gazette , Volume 80 , Issue 488 , July 1996 , pp. 279 - 285
Copyright
Copyright © The Mathematical Association 1996

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References

1 Nickalls, R.W.D., A new approach to solving the cubic: Cardan’s solution revealed, Math. Gaz. 77 (November 1993) pp. 354–359.Google Scholar
2 van der Waerden, B.L., Modem algebra, Vol 1, Fredrick Ungar Publishing Co., New York (1953).Google Scholar