Alec Armstrong	Posted on Tuesday, 29 April, 2003 - 04:55 pm: Are there any complex roots to the equation x3 -1? (I know that there are real roots at -1,0,+1.) For x4 I know that these are at -1,+1,-i and +1. I also believe for x2 -1 that there are no complex roots? (Only at -1 and +1.) Many thanks!
David Loeffler	Posted on Tuesday, 29 April, 2003 - 05:00 pm: Alec, Do you know about the factor theorem? It implies that a polynomial of degree n can't have more than n roots (real or complex), so in each case you have given all the roots of the equation. David
Alice Thompson	Posted on Tuesday, 29 April, 2003 - 05:43 pm: For x3 -1, -1 and 0 are not roots. The two complex roots are $-0.5+i\sqrt{3/2}$ and $-0.5-i\sqrt{3/2}$.
David Loeffler	Posted on Tuesday, 29 April, 2003 - 06:06 pm: Good point. Well spotted, Alice. I misread Alec's first equation as x3 - x instead of x3 - 1. David