Can someone please help me solve this polynomial equation?

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rogermiranda
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Can someone please help me solve this polynomial equation?

Postby rogermiranda » Sun Sep 26, 2010 4:31 pm

I have x^6 - 1=0
After the rational roots test, I have the factors of (x+1)(x-1).
So, after doing the synthetic division with these factors I am left with x^4 + x^2 + 1.
Now I am stuck. This equation does not factor, and it is not a quadratic. How do I move forward from here?
The roots by the way are 1,-1, and one plus or minus square root of 3 i divided by two and negative one plus or minus square root of 3 i divided by two. Please help! :confused:

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stapel_eliz
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Postby stapel_eliz » Sun Sep 26, 2010 10:26 pm

Have you covered deMoivre's formula yet? Or are you maybe supposed to solve the "quadratic" (x2)2 + (x2) + 1, and then solve the quadratics that result? :wink:

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Martingale
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Re: Can someone please help me solve this polynomial equatio

Postby Martingale » Sun Sep 26, 2010 11:22 pm

rogermiranda wrote:I have x^6 - 1=0
After the rational roots test, I have the factors of (x+1)(x-1).
So, after doing the synthetic division with these factors I am left with x^4 + x^2 + 1.
Now I am stuck. This equation does not factor, and it is not a quadratic. How do I move forward from here?
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