- #1
bob1182006
- 492
- 1
Factor a 4th order polynomial (Solved)
Find the roots of:
[tex] x^5-1=0[/tex]
Polynomial long division.
[tex] x^5-1 = (x-1)(x^4+x^3+x^2+x+1) = 0[/tex]
[tex] x^4+x^3+x^2+x+1 = (x^2+1)^2+x^3+x-x^2[/tex]
[tex] (x^2+1)^2+x^3+x-x^2 = (x^2+1)^2+x(x^2+1)-x^2[/tex]
Stuck at this point, I just can't seem to factor out something useful.
I know all of the roots are complex but I need to be able to solve the problem without a computer.
Homework Statement
Find the roots of:
[tex] x^5-1=0[/tex]
Homework Equations
Polynomial long division.
The Attempt at a Solution
[tex] x^5-1 = (x-1)(x^4+x^3+x^2+x+1) = 0[/tex]
[tex] x^4+x^3+x^2+x+1 = (x^2+1)^2+x^3+x-x^2[/tex]
[tex] (x^2+1)^2+x^3+x-x^2 = (x^2+1)^2+x(x^2+1)-x^2[/tex]
Stuck at this point, I just can't seem to factor out something useful.
I know all of the roots are complex but I need to be able to solve the problem without a computer.
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