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

Algebra ->  Equations -> SOLUTION: x^4 - x^3 + x^2 - x + 1 = 0      Log On


   

Question 1089213: x^4 - x^3 + x^2 - x + 1 = 0
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
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°).