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Putnam 1999 B2

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December 22, 2012
Putnamalgebrapolynomialquadraticscalculusderivativecollege contests

Problem Statement

Let P(x)P(x) be a polynomial of degree nn such that P(x)=Q(x)P′′(x)P(x)=Q(x)P^{\prime\prime}(x), where Q(x)Q(x) is a quadratic polynomial and P′′(x)P^{\prime\prime}(x) is the second derivative of P(x)P(x). Show that if P(x)P(x) has at least two distinct roots then it must have nn distinct roots.
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