- #1
VeeEight
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Homework Statement
Find the roots to the polynomial x4+x+1
this is a problem I am stuck with for my algebra class
Homework Equations
there are a few tricks I have learned for finding roots like taking conjugates and rewriting using fundamental theorem of algebra but we haven't worked on this stuff too much
The Attempt at a Solution
by fundamental theorem of algebra, we can write x4+x+1 = (x-a)(x-b)(x-c)(x-d) for some complex numbers a,b,c,d
so the roots a,b,c,d have to follow the equations:
a + b + c + d = 0
ad + ab + bd + cd + bc = 0
abd + bdc + acd + abc = 1
abcd = 1
other than that I do not know what else to do to find the roots