SOLUTION: Find all complex solutions of the equation: X^4-X^3+X^2-x=0.

Question 436866: Find all complex solutions of the equation: X^4-X^3+X^2-x=0.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find all complex solutions of the equation:
X^4-X^3+X^2-x=0.
Factor:
x(x^3-x^2+x-1) = 0
---
So x= 0 is a Real root.
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Since the coefficients add to zero, x=1 is a Real root.
Use synthetic division:
1)....1....-1....1....-1
.......1.....0....1....|..0
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Quotient: x^2+1
---
Factor:
(x-i)(x+i) = 0
x = i or x = -i
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Solutions: x= 0, or 1, or i, or -i.
Cheers,
Stan H.

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