Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T18:10:13.332Z Has data issue: false hasContentIssue false

On the structure of polynomial roots

Published online by Cambridge University Press:  21 June 2021

R. W. D. Nickalls*
Affiliation:
10 Queens Parade, CheltenhamGL50 3BB e-mail: [email protected]

Extract

This Article explores how root multiplicity and polynomial degree influence the structure of the roots of a univariant polynomial. After setting up the notation, we draw upon a result derived in [1], and show that all polynomial roots have a common underlying structure comprising just five parameters. Finally we present some examples involving the lower polynomials.

Type
Articles
Copyright
© Mathematical Association 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Nickalls, R. W. D., A new bound for polynomials when all the roots are real, Math. Gaz. 95 (November 2011) pp. 520526.CrossRefGoogle Scholar
Nickalls, R. W. D., A new approach to solving the cubic: Cardan’s solution revealed. Math. Gaz. 77 (November 1993) pp. 354359.CrossRefGoogle Scholar
Holmes, G. C., The use of hyperbolic cosines in solving cubic polynomials, Math. Gaz. 86 (November 2002) pp. 473477.CrossRefGoogle Scholar
Nickalls, R. W. D., The quartic equation: invariants and Euler’s solution revealed, Math. Gaz. 93 (March 2009) pp. 6675.CrossRefGoogle Scholar
Nickalls, R. W. D., The quartic equation: alignment with an equivalent tetrahedron, Math. Gaz. 96 (March 2012) pp. 4955.CrossRefGoogle Scholar
Nickalls, R. W. D., The complementary cubic, Math. Gaz. 104 (March 2020) pp. 155158.CrossRefGoogle Scholar