Authors and affiliations
The University of Sydney, 2006, Australia
Warrane College, The University of New South Wales, 1465, &KvB Institute of Technology, North Sydney, 2060, Australia
The Cardano cubic, , has one real zero and a complex conjugate pair. The real zero is given by or , in which are important parameters that feature in the roots of all Cardano cubics. They are functions of the coefficients of the complex conjugate pairs. We find that
with and 11° < < 60° for real zero. Furthermore, for integer, the range of is reduced to 52° < < 60°, where the functional surfaces suggest the reason the integer would only be compatible with an irrational value of . This is verified algebraically.
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Cite this paper
Leyendekkers, J. & Shannon, A. (2000). Analysis of the roots of some Cardano cubes. Notes on Number Theory and Discrete Mathematics, 6(4), 113-117.