SOLUTION: x^4 - x^3 + x^2

SOLUTION: x^4 - x^3 + x^2 - x + 1 = 0

Question 1089213: x^4 - x^3 + x^2 - x + 1 = 0
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
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If you multiply both sides of your equation by (x+1), you will get the equation

x^5 + 1 = 0,   or   x^5 = -1.


Its roots are the roots of degree 5 of -1   (one real root -1 and the others are complex roots).


Therefore, the roots of the original equation are all four complex roots of the degree 5  of -1.


They are 

1)  cos(36�) + i*sin(36�);

2)  cos(108�) + i*sin(108�);

3)  cos(252�) + i*sin(252�);

4)  cos(324�) + i*sin(324�).

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