(iii/.
rim
HW due Apr 4
Tao Ju
April 4, 2014
Problem 25
Prove that [Fe : Q} is innite. FC is the eld of constructible reals (straight edge and compass).
Proof:
It is clear 27x72 6 FC for any n, which is a root of (102n 2 = 0. Let f(.13) = $2 2,
HW due Mar 5
Tao Ju
March 5, 2014
Problem 20
Let at be transcendental over Zg. Let F = Z2 (a) and let p(a:) = $2 oz.
(a) Prove that p is irreducible over F.
(b) Prove that if ,8 is a root of p in some extension eld, then p(:r) :2 (a: ,8)?
(0) Su