Inspired by Calvin Lin

Algebra Level 5

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 $a$ .