splitting field problem
2007-01-04 4:13 pm
Determine the splitting field over Q of the polynomial x^4-5x^2+6 and find the degree over Q
回答 (1)
2007-01-04 9:01 pm
✔ 最佳答案
x^4-5x^2+6 = (x^2 -3)(x^2 -2) =(x -rt3 )(x +rt3)(x -rt2)(x +rt2)x^2 -3 and x^2 -2 are minimal irreducible polynomial over Q and both of them are of degree 2.
Hence, the splitting field is Q( rt3 , rt2) and the degree over Q is 2x2=4, where rt3 and rt2 are the positive square root of 3 and 2 respectively.
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