Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

Mathematical Way to Find the Roots of the Cubic?

I'm trying to find a way to figure out the roots of

... The roots are supposedly

and

.

I find it amazing how the roots of this polynomial can be expressed with cosines. Is there a mathematical way that can solve this?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical Way to Find the Roots of the Cubic?

Does your substitution in the other thread work? If it did not then maybe you need a different substitution for each one.

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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: Mathematical Way to Find the Roots of the Cubic?

Substituting

with

unfortunately does not work. But perhaps you have to substitute

with something different, such as

and then substitute

with something else... Just a thought.

I wonder if Vieta's Trigonometric Solution will work for this... It should. But it may not give me the answer in the format that I would like...