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Algebra Level 5

If the polynomial \(f(x) = 4x^{4} - ax^{3} + bx^{2} -cx + 5\) where \(a,b,c \in \mathbb{R}\) has four positive real roots say \(r_{1},r_{2},r_{3},r_{4}\) such that \(\frac{r_{1}}{2} + \frac{r_{2}}{4} + \frac{r_{3}}{5} + \frac{r_{4}}{8} = 1\) .Then find the value of \(a\)

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