Considering $L$ as the splitting field of $x^4-x^2-1$ over $\mathbb{Q}$, determine the group Gal$(L/\mathbb{Q})$.
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1What have you tried? Where do you need help? For example since you need a splitting field obviously you should find the 4 roots first – Μάρκος Καραμέρης Apr 03 '19 at 18:27
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It seems that the splitting field is $\mathbb{Q}(\sqrt{5},i)$, and I can not figure out whether it is $K_4$ or $C_4$. – Albert-zhang Apr 03 '19 at 18:35
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Also see this question, with $n=2$, or Keith Conrad's article on Galois groups of cubics and quartics (very well explained). – Dietrich Burde Apr 03 '19 at 19:02