Cubic equations with 2 Roots in the interval [-1, 1]
DOI:
https://doi.org/10.32603/2071-2340-2024-2-30-38Keywords:
cubic equation, quartic equation, real-rooted polynomials, intervalAbstract
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.
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
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Published
2024-08-30
Issue
Section
Algorithmic mathematics and mathematical modelling
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
[1]
H. Ruhland, “Cubic equations with 2 Roots in the interval [-1, 1]”, Computer Tools in Education, no. 2, pp. 30–38, Aug. 2024, doi: 10.32603/2071-2340-2024-2-30-38.
