- #1
giulio_hep
- 104
- 6
- TL;DR Summary
- irreducible P with roots in extension L of degree <= 2
I'm not sure the following passage is so trivial as it was supposed to be: I mean, what does exactly prove it? That's my question.
The step is the following:
if ##P## has a root ##\alpha## in ##\mathbf L## - an extension of ##\mathbf K## of degree <= ##\frac n 2## where n is the degree of ##P## over ##\mathbf K## - the minimal polynomial of ##\alpha## over ##\mathbf K## divides ##P##.
While it looks sort of acceptable/obviously true, I'm not sure of what would really be its proof.
Thank you.
The step is the following:
if ##P## has a root ##\alpha## in ##\mathbf L## - an extension of ##\mathbf K## of degree <= ##\frac n 2## where n is the degree of ##P## over ##\mathbf K## - the minimal polynomial of ##\alpha## over ##\mathbf K## divides ##P##.
While it looks sort of acceptable/obviously true, I'm not sure of what would really be its proof.
Thank you.
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