Cubic equations with 2 Roots in the interval [-1, 1]

  • Helmut Ruhland Independent Researcher, Santa Fe, La Habana, Cuba
DOI: https://doi.org/10.32603/2071-2340-2024-2-30-38
Keywords: cubic equation, quartic equation, real-rooted polynomials, interval

Abstract

The conditions for cubic equations, to have 3 real roots and 2 of the roots lie in the closed interval [-1, 1] are given. These conditions are visualized. This question arises in physics e.g. the theory of tops. 

Author Biography

Helmut Ruhland, Independent Researcher, Santa Fe, La Habana, Cuba

Independent Researcher, Santa Fe, La Habana, Cuba, helmut.ruhland50@web.de

References

E. M. Prodanov, “On the cubic equation with its Siebeck-Marden-Northshield triangle and the quartic equation with its tetrahedron,” Journal of Computational Science, vol. 73, p. 102123, 2023; doi:10.1016/j.jocs.2023.102123

L. N. Hand and J. D. Finch, “Chapter 3. The Motion of Rigid Bodies,” in Analytical Mechanics, Cambridge, England: Cambridge University Press, 1998. [Online]. Available: https://www.damtp.cam.ac.uk/user/tong/dynamics/three.pdf

Published
2024-08-30
How to Cite
Ruhland, H. (2024). Cubic equations with 2 Roots in the interval [-1, 1]. Computer Tools in Education, (2), 30-38. https://doi.org/10.32603/2071-2340-2024-2-30-38
Issue
No 2 (2024)
Section
Algorithmic mathematics and mathematical modelling