I need to show that the Galois extension (the separable and normal) extension of the polynomial $f(x) \in \Bbb Q[x]$: $f(x)=x^5-10x+5$ its Galois group is isomorphic to $S_5$
How to do it when I can't even find it's roots?
2026-03-28 16:58:13.1774717093
The Galois group corresponded to a polynomial of 5 degree
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It has exactly $3$ real roots, and $5$ is prime, so it follows.