Thread: poly

Hi

how can I find the basis of [L:Q] for \sqrt {11+5\sqrt{11}}

thank you

Originally Posted by jerad

Hi

how can I find the basis of for

thank you

Let and we have .

(ask if you want to see how I got this).

Thus , so our basis is .

Hi

Thank you for your help.

But I posted the question wrong. I need to find the minimum polynomial for
\sqrt {11+5\sqrt{11}}. Then I am finding the zeros of the minimum poly. From that I find the splitting field as [L:Q]=[Q(alpha,beta):Q).I got 16 is that correct? And then I don't know how to find the basis for [L:Q]. If you can give me some ideas that would be great.

Thank you

Hi

I posted the question wrong. I need to find the minimum polynomial for
\sqrt {11+5\sqrt{11}}. Then I am finding the zeros of the minimum poly. From that I find the splitting field as [L:Q]=[Q(alpha,beta):Q).I got 16 is that correct? And then I don't know how to find the basis for [L:Q]. If you can give me some ideas that would be great.

Thank you

Originally Posted by jerad

Hi

I posted the question wrong. I need to find the minimum polynomial for
\sqrt {11+5\sqrt{11}}. Then I am finding the zeros of the minimum poly. From that I find the splitting field as [L:Q]=[Q(alpha,beta):Q).I got 16 is that correct? And then I don't know how to find the basis for [L:Q]. If you can give me some ideas that would be great.

Thank you

I posted the minimum polynomial in my last post.

yes I also found the minimum polynomial and I worked out the zeros of the minimum polynomial. The zeros cojugate.alpha=\sqrt {11+5\sqrt{11}}and beta=\sqrt {11-5\sqrt{11}} .
and I got [L:Q]=16.Is that correct? I don't really know how to fine the basis of Q(\alpha ,\beta ).
Could you help with this.

Thank you