# Polynomials going crazy!

Algebra Level 5

The polynomial $$f(x) = x^{2007} + 17x^{2006} + 1$$ has distinct roots $$r_1, r_2,\ldots, r_{2007}$$. A polynomial $$P$$ of degree 2007 has the property that $$P \left( r_j + \dfrac1{r_j} \right) = 0$$ for $$j = 1,2,\ldots,2007$$.

Compute $$\dfrac{259}{17} \times \dfrac{P(1)}{P(-1)}$$.

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