# splitting field

• Apr 11th 2010, 05:18 PM
apple2009
splitting field
Determine the splitting field and its degree over Q for p(x)=x^4+4.
(I did not really understand the splitting field)
• Apr 11th 2010, 05:55 PM
NonCommAlg
Quote:

Originally Posted by apple2009
Determine the splitting field and its degree over Q for p(x)=x^4+4.
(I did not really understand the splitting field)

the spilitting field of a polynomial over a field F is the smallest field which contains all the roots of that polynomial. so if $a_1, \cdots , a_n$ are the roots, then the spilitting field would be $F(a_1, \cdots , a_n).$

can you solve the problem now?