I have the four roots but I am unsure how to proceed next, and how to show the degree of the extension over Q is 8.
how would I find the splitting field of $x^4+13$?
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field-theory
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2Do you know what "splitting field" means? – 2012-10-23
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0it's the smallest field extension in which the polynomial splits, right? I have the 4 roots (via factoring), but not sure what to do next – 2012-10-23
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0Hint: $(x^4+13)(x^4-13) = x^8 -169$. So a root of your polynomial is also... – 2012-10-23