4
$\begingroup$

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.

  • 2
    Do you know what "splitting field" means?2012-10-23
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    it's the smallest field extension in which the polynomial splits, right? I have the 4 roots (via factoring), but not sure what to do next2012-10-23
  • 0
    Hint: $(x^4+13)(x^4-13) = x^8 -169$. So a root of your polynomial is also...2012-10-23

1 Answers 1