# Math Help - Splitting fields

1. ## Splitting fields

Find the degree of the splitting field for the polynomial x^4 + 19 over the field Q(root19).

2. Originally Posted by Becks
Find the degree of the splitting field for the polynomial x^4 + 19 over the field Q(root19).

$x^4+19=(x^2+\sqrt{19}\,i)(x^2-\sqrt{19}\,i)$ ; since the field $\mathbb{Q}(\sqrt{19})$ is a real field, the eement $i=\sqrt{-1}$ is not contained in it...try to take it from here.

Tonio

3. What do you mean by a real field?

4. Originally Posted by Becks
What do you mean by a real field?

A real field: $\mathbb{Q}(\sqrt{19})\subset \mathbb{R}$ .

Tonio

5. Do you know what the degree would be...so once i have worked it out, i will know i have done it correctly...