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On rational-derived quartics
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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