- #1

mathjam0990

- 29

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Let f(x)=x

Find the splitting field and Galois group for f(x) over ℚ

Here is what I have written out so far. If I have found the splitting field E correctly, have I proceeded with the Gal(E/F) group correctly?

Also, how would I go about finding the roots of this equation by hand without a calculator?

If anyone could help me out with the answer and a detailed explanation to follow that would be very helpful. Thank you.

View attachment 5498

^{4}-2x^{2}+9Find the splitting field and Galois group for f(x) over ℚ

Here is what I have written out so far. If I have found the splitting field E correctly, have I proceeded with the Gal(E/F) group correctly?

Also, how would I go about finding the roots of this equation by hand without a calculator?

If anyone could help me out with the answer and a detailed explanation to follow that would be very helpful. Thank you.

View attachment 5498