Question 104
The polynomial $f(x) = x^{2007} + 17 x^{2006} + 1$ has distinct zeroes $r_1, \ldots, r_{2007}$. A polynomial $P$ of degree $2007$ has the property that $P\left(r_j + \frac{1}{r_j}\right) = 0$ for $j = 1, \ldots, 2007$. Determine the value of $\frac{P(1)}{P(-1)}$.