If it were in Q then the polynomial would be p(x) = x - π^2, but I don't know if being over Q(π^3) changes that. I think that when you compare the fields you get degree 1, but again, I'm not completely sure.

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- Mar 26th 2012, 11:11 AMlteece89Find the minimal polynomial for a = π^2 over Q(π^3)
If it were in Q then the polynomial would be p(x) = x - π^2, but I don't know if being over Q(π^3) changes that. I think that when you compare the fields you get degree 1, but again, I'm not completely sure.

- Mar 26th 2012, 11:33 AMSylvia104Re: Find the minimal polynomial for a=π^2 over Q(π^3)
If the extension is the minimal polynomial is

- Mar 26th 2012, 12:54 PMlteece89Re: Find the minimal polynomial for a = π^2 over Q(π^3)
Is this because the minimal polynomial needs to be degree three?

- Mar 26th 2012, 02:40 PMSylvia104Re: Find the minimal polynomial for a=π^2 over Q(π^3)
The minimal polynomial here is the monic polynomial

*of minimal degree*with coefficients in such that If has degree or is of the form or where clearly these cannot be