Let x 4 + ax 2 +b K[x] (with char K 2) be irreducible with

Let x⁴ + ax² +b ϵ K[x] (with char K ≠ 2) be irreducible with Galois group G.

(a) If b is a square in K, then G = V.

(b) If b is not a square in K and b(a² - 4b) is a square in K, then G ≅ Z₄.

(c) If neither b nor b(a² - 4b) is a square in K, then G ≅ D₄.