I would like to know a proof for the "bounds on zeros" theorem.  Thanks

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Request for Question Clarification by maniac-ga on 04 Oct 2003 09:26 PDT

Hello Justinmaurer,

If you are looking for a prompt answer, I suggest
- you describe *which* "bounds on zeros" you are referring to. There
are a number of disciplines that this could apply to.
- determine if one or a few URL's would be an appropriate answer. If
not, I suggest you revise the price offered.

  --Maniac

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Clarification of Question by justinmaurer-ga on 06 Oct 2003 20:42 PDT

I would think one URL would be appropriate enough that would show me
the proof for it.  The bounds on zeros theorem says:

 Let f denote a polynomial function whose leading coefficient is 1.

 f(x)=x^n + a sub(n-1)x^(n-1)+...+a sub(1)x+a0

 A bound M on the zeros of f is the smalle of the two numbers

Max {1,|a sub(0)|+|a sub(1)|+...+|a sub(n-1)|}, 1 + Max{|a sub(0)|,|a
sub(1)|,..., |a sub(n-1)|}

Where Max {  } means "choose the largest entry in {   }."

That is what the theorem says, I was looking to see what it is derived
from or what the mathematical proof is.

Thanks for any help at all :)