# Math Help - galois group

1. ## galois group

Find the Galois group for f(x) =x^4-2x²+9 over Q.
I don’t really know how to find the Galois group; can someone explain to me how to find it? Thank you.

2. Originally Posted by apple2009
Find the Galois group for f(x) =x^4-2x²+9 over Q.
I don’t really know how to find the Galois group; can someone explain to me how to find it? Thank you.
To find the Galois group for quartic polynomial over Q, you need first to find the resolvent cubic of f(x) and its discriminant.

If the resolvent cubic of f(x) splits completely, then its Galois group is $V_4 \cong \{e, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)\}$.