# Math Help - splitting field

1. ## 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)

2. 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?