Do as asked. a. Give the smallest extension of Q that contains all the zeros of x4 - 2x - 15. b. Let m, n be positive integers. Show that the real numbers e" and we are algebraic over Q(e"). [Here, e is Euler's number.] c. Let a7+43. Show that [Q(a): Q] = 2. d. Let p be a prime. Give all the subfields of F220 and sketch its subfield lattice