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wu :: forums    riddles    medium (Moderators: Eigenray, Grimbal, ThudnBlunder, towr, william wu, Icarus, SMQ)    Sharp Lower Bound « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Sharp Lower Bound  (Read 704 times) Michael Dagg Senior Riddler     Gender: Posts: 500 Sharp Lower Bound   « on: May 1st, 2009, 9:44am » Quote Modify 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). IP Logged Regards, Michael Dagg Obob Senior Riddler     Gender: Posts: 489 Re: Sharp Lower Bound   « Reply #1 on: May 1st, 2009, 11:55am » Quote Modify 3^n, satisfied by p(x) = (x+1)^n IP Logged Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: Sharp Lower Bound   « Reply #2 on: May 1st, 2009, 3:05pm » Quote Modify I get the same result as Obob.   A thread which appeared earlier might be helpful:   http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_med ium;action=display;num=1179865908 IP Logged Obob Senior Riddler     Gender: Posts: 489 Re: Sharp Lower Bound   « Reply #3 on: May 1st, 2009, 3:15pm » Quote Modify Ha, I totally forgot about that one. IP Logged Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: Sharp Lower Bound   « Reply #4 on: May 1st, 2009, 4:19pm » Quote Modify on May 1st, 2009, 3:15pm, 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! IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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