# Sum of roots of polynomial

Algebra Level 5

Consider the polynomial $$p(x)$$ defined as:- $p(x)=x^4+x^3+2x^2+3x+1$ Let $$r_1,r_2,r_3,r_4$$ be the roots of $$p(x)$$ then the value of $\left( \sum_{i \neq j} \frac{1}{ (1-r_i)(1-r_j) } \right) \left(\sum_{i=1}^4 \frac{1}{1-r_i} \right)$ can be expressed as $$\frac{a}{b}$$ where $$gcd(a,b)=1$$ find $$a+b$$

Details and assumptions:- I have used the notation $$\sum(\frac{1}{(1-r_i)(1-r_j)}$$ to represent the sum of all possible products of the form $$\frac{1}{(1-r_i)(1-r_j)}$$ taken two at a time and $$i \neq j$$ (i think it also called cyclic sum)

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