# Let's see how good you are at polynomial transformation

Algebra Level 4

Let $$r_{1}, r_{2}, ..., r_{2014}$$ be the roots, not all necessarily distinct, of the polynomial $$x^{2014} + x^{20} + x^{14} + 2014.$$ The polynomial with roots

$\frac{r_{2}+r_{3}+\cdots+r_{2014}-r_{1}}{r_{2}^{2}+r_{3}^{2}+\cdots+r_{2014}^{2}-r_{1}^{2}}, \frac{r_{1}+r_{3}+\cdots+r_{2014}-r_{2}}{r_{1}^{2}+r_{3}^{2}+\cdots+r_{2014}^{2}-r_{2}^{2}}, \cdots, \frac{r_{1}+r_{2}+\cdots+r_{2013}-r_{2014}}{r_{1}^{2}+r_{2}^{2}+\cdots+r_{2013}^{2}-r_{2014}^{2}}$

has the form $$ax^{b} + x^{c} + x^{d} + e$$, for some positive integers $$a, b, c, d,$$ and $$e$$. Find $$a+b+c+d+e.$$

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