I don't think you can find an exact value for alpha. But you can use Rouche's theorem to show that there is exactly one root inside , provided that n is reasonably large (say n>=6). The result is false for n=2 and n=3. You can't use Rouché's theorem directly, because the polynomial has a root at z=1. But you can apply it to a slightly smaller circle, on which will be less than .)
Guide to latex:
http://www.goiit.com/posts/list/community-shelf-a-guide-to-latex-48056.htm
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, provided that n is reasonably large (say n>=6). The result is false for n=2 and n=3. 
will be less than 
.)
