# find roots

**Algebra**Level 5

Given the polynomial \[G(x)=16x^4+8x^3+4x^2+2x+1\] has roots \(\quad a_1,a_2,a_3,a_4 \quad\)that can be written as \(\quad x_n (\cos (z_n\pi )+i\sin (z_n\pi))\quad\), where \( 0 \leq z_i < 2 \pi \). \[\sum_{n=1}^4 \dfrac{x_n}{z_n}\] can be written as \(\quad\dfrac{a}{b}\quad\) where a and be are coprime integers. find \(a+b\)