Inspired by Calvin Lin

Algebra Level 4

If the polynomial \(f(x)=4x^4-a.x^3+b.x^2-c.x+5\) where \(a,b,c \in \mathbb{R}\) has \(4\) positive real zeroes(roots) say \(r_1,r_2,r_3, \ and \ r_4\), such that \[\frac{r_1}{2}+\frac{r_2}{4}+\frac{r_3}{5}+\frac{r_4}{8}=1\] Find the value of \(a\).