# How to work out a Galois Group of a polynomial

• Oct 29th 2010, 06:29 AM
phillips101
How to work out a Galois Group of a polynomial
How do I do it with a horrible polynomial? I know how to construct it when the polynomial is simple, such as x^3=7, but what about when the poly is x^4+2x+3=0, for instance? (Random example, I don't actually need the answer). The method I have for solving the first polynomial relies directly on it being of a very simple form.

Help would be appreciated.
• Oct 29th 2010, 07:09 AM
tonio
Quote:

Originally Posted by phillips101
How do I do it with a horrible polynomial? I know how to construct it when the polynomial is simple, such as x^3=7, but what about when the poly is x^4+2x+3=0, for instance? (Random example, I don't actually need the answer). The method I have for solving the first polynomial relies directly on it being of a very simple form.

Help would be appreciated.

Go here FT --- J.S. Milne , download that PDF file from the top of the page, and read in page 38.

Tonio