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 October 9th, 2011, 06:54 PM #1 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 multiple choice Let $f(x)$ be the monotonic polynomial of $(2m-1)$ degree where m belongs to natural no., then equation $f(x)+f(3x)+f(5x)+. . . . . .f((2m-1)x)= 2m-1$ has: A) At least one real root B) (2m-1) real roots C) exactly one real root D) none of these
 October 10th, 2011, 01:04 PM #2 Global Moderator   Joined: May 2007 Posts: 6,786 Thanks: 708 Re: multiple choice Sum of monotonic polynomials is monotonic. Being polynomials, they have to be strictly increasing (or decreasing). Net result exactly one real root.

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