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OpenStudy (anonymous):
find the degree of splitting field of x5-3x3+x2-3 over Q
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OpenStudy (anonymous):
first factor the expression.
OpenStudy (anonymous):
(x+1)(x-sqrt 3 ) ( x+sqrt 3) (x^2 - x + 1)
OpenStudy (anonymous):
so the degree of the splitting field is 2. Don't ask me how, just google it.
OpenStudy (anonymous):
theres only one rational root though
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OpenStudy (anonymous):
which is the one rational root?
OpenStudy (anonymous):
1
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