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On rational-derived quartics

Published online by Cambridge University Press:  17 April 2009

R.H. Buchholz  and
S.M. Kelly
R.H. Buchholz
Affiliation:
Department of Defence Po Box 4924 Kingston, ACT 2604Australia e-mail: ralph@defcen.gov.au
S.M. Kelly
Affiliation:
Department of Defence Po Box 4924 Kingston, ACT 2604Australia e-mail: ralph@defcen.gov.au
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Abstract

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We present a characterisation of all quartic polynomials with exactly three distinct roots and the property that it and all its derivatives have rational roots. It turns out that there are an infinite number of distinct such quartics, each of which corresponds to a point on a related elliptic curve. Furthermore the collection of these points forms a proper subgroup of the group of rational points on the curve.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 1 , February 1995 , pp. 121 - 132
Copyright
Copyright © Australian Mathematical Society 1995

References

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