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        riddles >> medium >> Sharp Lower Bound
        
(Message started by: Michael Dagg on May 1^st, 2009, 9:44am)

Title: Sharp Lower Bound
Post by Michael Dagg on May 1^st, 2009, 9:44am

Inspired from an other problem here:

Suppose that all the coefficients of

p(x) = x^n + a_{n-1} x^{n-1} + ... + a_1 x + 1

are positive and the n roots of p are real.

Determine a sharp lower bound for p(2).

Title: Re: Sharp Lower Bound
Post by Obob on May 1^st, 2009, 11:55am

[hide]3^n, satisfied by p(x) = (x+1)^n[/hide]

Title: Re: Sharp Lower Bound
Post by Aryabhatta on May 1^st, 2009, 3:05pm

I get the same result as Obob.

A thread which appeared earlier might be helpful:

[hide] http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1179865908 [/hide]

Title: Re: Sharp Lower Bound
Post by Obob on May 1^st, 2009, 3:15pm

Ha, I totally forgot about that one.

Title: Re: Sharp Lower Bound
Post by Aryabhatta on May 1^st, 2009, 4:19pm

on 05/01/09 at 15:15:45, Obob wrote:

Ha, I totally forgot about that one.

Not unreasonable, considering the fact that I almost forgot it too, and I started that thread!