 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2007/b/b2/i/solution

All sixth roots of unity lie in

Q (ζ_{6})

, with

ζ_{6} = (1 + - 3) /2

x^{2} - x + 1

has no rational root, so

K = Q (- 3), [K : Q] = 2 .

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