Thread: splitting field L

B is a real number Sqrt(7 + 2*sqrt(7))

basically i have done the parts of finding the minimal polynomial mu of B over Q, and all the zeros of mu.

but i got stuck on the part where i need to find the degree [L :Q] and the basis for L over Q

Where L is the splitting field of mu over Q

can anyone help me find the degree and basis

thanks

Originally Posted by dopi

B is a real number Sqrt(7 + 2*sqrt(7))

basically i have done the parts of finding the minimal polynomial mu of B over Q, and all the zeros of mu.

but i got stuck on the part where i need to find the degree [L :Q] and the basis for L over Q

Where L is the splitting field of mu over Q

can anyone help me find the degree and basis

thanks

Let .
Find the zeros of this polynomial and form the splitting field.

Originally Posted by ThePerfectHacker

Let .
Find the zeros of this polynomial and form the splitting field.

i found the zeros as




so i tried , where i got , so is the splitting field L of mu over Q = .

is the degree[L,:Q] = 4x4 = 16
and the basis for L over Q { }
and the order of the galois group

Originally Posted by dopi

i found the zeros as




so i tried , where i got , so is the splitting field L of mu over Q = .

is the degree[L,:Q] = 4x4 = 16
and the basis for L over Q { }
and the order of the galois group

The splitting field is .

is the degree[L,:Q] = 4x4 = 16
and the basis for L over Q { }
and the order of the galois group [/QUOTE]

i was wondering are these correct?