all numbers refer to exercises and not computer

Question

All numbers refer to exercises (and not "computer exercises") in Gallian. §22: 8, 16, 22, 24, 28, 36.

In addition:

Problem 1: Let a be a complex root of the polynomial x⁶ + x³ + 1. Find all homeomorphisms σ: Q(a) → C over Q. (HINT: the polynomial is a factor of x⁹-1.)

Problem 2: We say that a ?eld extension E/F is quadratic if [E: F] = 2. Prove that every quadratic extension of F is normal.