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2007 Algebra #10: 2007 Distinct Zeroes

Source:

June 21, 2012

algebrapolynomial

Problem Statement

The polynomial

f(x)=x^{2007}+17x^{2006}+1

has distinct zeroes

r_1,\ldots,r_{2007}

. A polynomial

P

of degree

2007

has the property that

P\left(r_j+\dfrac{1}{r_j}\right)=0

for

j=1,\ldots,2007

. Determine the value of

P(1)/P(-1)

.

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