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)

×

Problem Loading...

Note Loading...

Set Loading...