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Crescendo

Guest

Find the roots of the following polynomial

Is there a way to find the roots of x^3+x^2-10x-8=0?

I've tried substituting x with

but I got a really weird answer.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Find the roots of the following polynomial

Here is one way by completing the cube:

http://www.mathisfunforum.com/search.ph … 1038166535

And there is a formula in terms of the coefficients.

But as I have been saying to evene and corrupted, it is much easier to do numerically.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Find the roots of the following polynomial

The link doesn't work.

If you wish to express the roots as the sums of cosines, then you use a prime number of the form p=6m+1. With m as the "number of cosines" that you use. So for you, we have p=31=6m+1. Thus, m=5. Meaning the roots are

Note that this doesn't work for any cubic as the constant has to be a specific term in order to be able to express the roots as the pth roots of unity.

Last edited by evene (2016-10-26 15:20:06)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Find the roots of the following polynomial

Hi;

I am sorry, try http://www.mathisfunforum.com/viewtopic … 00#p198900

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.