Can someone please help me solve this polynomial equation?

[rogermiranda]

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!

[stapel_eliz]

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?

[Martingale]

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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