homework11

# homework11 - Q α Q(d Find the minimal polynomial of α...

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Math 113 Section 5 Homework #11 Fall 2010 Due: Friday, December 3 1. Section 13.1, Exercise 5: Suppose α is a rational root of a monic polynomial in Z [ x ] . Prove that α is an integer. 2. Let p and q be distinct prime integers. (a) Show that Q ( p, q ) = Q ( p + q ) . (b) Find the minimal polynomial of p + q . 3. Let α = ñ 2 + 2 . (a) Find the minimal polynomial of 2 over Q . (b) Find the minimal polynomial of α over Q ( 2) . (c) Determine
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Unformatted text preview: [ Q ( α ) : Q ] . (d) Find the minimal polynomial of α over Q . 4. Let 3 √ 2 be the real cube root of 2 . (a) Find the minimal polynomials of 3 √ 2 and i over Q . (b) Find the minimal polynomial of i over Q ( 3 √ 2) . (c) Show that Q ( i 3 √ 2) = Q ( i, 3 √ 2) . (d) Find the minimal polynomial of i 3 √ 2 over Q . 1...
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## This note was uploaded on 01/21/2012 for the course MATH 113 taught by Professor Ogus during the Fall '08 term at Berkeley.

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