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Mathematics
Linear and Abstract Algebra
Solution?: Quintic Equation from Physical System
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[QUOTE="danielFiuza, post: 6073206, member: 652397"] First time in this forum, so greetings to everyone! I am currently working with some physical models in the field of natural ventilation and I came across the following 5th order polynomial equation (quintic function): [I][B]$X^{5}+ C X - C =0$[/B] [/I] This is the steady state solution of a physical system of coupled ODEs. And I am interested in finding a explicit relationship for X = f(), (the roots in terms of C), possibly analytically. The values of X (that makes physical sense) needs to be real and between 0 and 1. Additionally, C is a constant (a time scale of my system), which need to be larger or equal than 0 (and to infinity). I can plot this equation numerically[B],[/B] but I was wondering if I can obtain a explicit/analytical solution of this equation for [B]C>=0 and X[0 1][/B]. I have been reading a little bit about quintic functions, and how some of them can be solved (this one seems to be in a similar way as Quintics in Bring–Jerrard form). If anyone could give me some insight about this equations or if it is possible an explicit solution for the root with the constrains C>=0 and X[0 1], I would be extremely grateful! Thanks in advance, Daniel EDIT: improved explanation of one line. [/QUOTE]
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Linear and Abstract Algebra
Solution?: Quintic Equation from Physical System
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