I have a 5th order, uni-variable, polynomial :(

As I understand the only way to solve this is to guess?

Since this is a real world equation, rather than something from a textbook, there really isn't any chance of me finding clean roots by guessing.

Is there any solution for polynomials in higher math?

  • $\begingroup$ Where is the equation? $\endgroup$ – NoChance Jun 16 '15 at 20:16
  • $\begingroup$ @EmmadKareem Oh it's got cosines in it, acceleration due to gravity and so on, it's not like I'm even working with integers. I was hoping that there was something in calculus that I had forgotten which offered me a solution to this. $\endgroup$ – Jonathan Mee Jun 16 '15 at 20:18
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    $\begingroup$ Lots of ways to approximate. There is no general quintic formula, though. $\endgroup$ – Ry- Jun 16 '15 at 20:25
  • $\begingroup$ If you only want real roots, you know there's at least one, and minitech's comment is probably your best bet. You should be able to determine how many real roots there are using calculus, and that will give you good clues on where to start your approximations from. $\endgroup$ – Todd Wilcox Jun 16 '15 at 20:27
  • $\begingroup$ This may be relevant: math.stackexchange.com/questions/540964/… $\endgroup$ – NoChance Jun 16 '15 at 20:29

There’s no general quintic formula like there is for lower-degree polynomials, but there are lots of ways to approximate roots.

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If you're looking for a solution (as opposed to a general method), Excel's Solver should work. The Non-Linear Solver will give at least one real root, and the Evolutionary Solver may give them all.

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  • $\begingroup$ Excel solver cringe $\endgroup$ – MichaelChirico Jun 16 '15 at 23:47

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