- #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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