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ISI B.Math(Hons.) Admission Test 2009 Problem 2

Source:

April 9, 2012

algebraequationcalculus

Problem Statement

Let

c

be a fixed real number. Show that a root of the equation

x(x+1)(x+2)\cdots(x+2009)=c

can have multiplicity at most

2

. Determine the number of values of

c

for which the equation has a root of multiplicity

2