[代數] 請問幾題代數，關於Galois group of polynomial

[Scape (non)]

Find the Galois group of the polyomial over Q

1. x^4 - 5x^2 + 6

2. x^3 - 6x^2 + 2

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推 jacky7987   :1. (x^2-3)(x^2-2)  Q(sqrt(2),sqrt(3)) 是splitting
→ jacky7987   :2. If f(x)=x^3+qx+r  and let D^2=-4q^3-27r^2
→ jacky7987   :if D^2 is a square in Q, then Gal=A_3
→ jacky7987   :if not, then Gal=S_3
推 jacky7987   :To transfer to the form just Let X=x-1/3