(a) Show that t = 33+1 2 and conclude that L = C().

Help with parts b,c,d please

 Let F = C(t) and let L = F(α), where α has minimal polynomial g = x3 − tx2 + (t − 3)x + 1.

(a) Show that t = α 3−3α+1 α2−α and conclude that L = C(α).

(b) Show that we can define a field automorphism σ : L → L by setting σ(α) = 1/(1 − α).

(c) Show that σ ∈ Gal(L/F).

(d) Show that L/F is Galois and that Gal(L/F) is the cyclic group of order 3.