Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
rogermiranda
Posts: 19
Joined: Fri Apr 30, 2010 6:01 pm
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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
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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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?
...
$x^4 + x^2 + 1=(x^2+x+1)(x^2-x+1)$