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2010 Algebra #9: Real Recursive Roots

Source:

July 15, 2012

algebrapolynomial

Problem Statement

Let

f(x)=cx(x-1)

, where

c

is a positive real number. We use

f^n(x)

to denote the polynomial obtained by composing

f

with itself

n

times. For every positive integer

n

, all the roots of

f^n(x)

are real. What is the smallest possible value of

c

?

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