1985 OIM Problems/Problem 3

Problem

Find the roots $r_1$ , $r_2$ , $r_3$ , and $r_4$ of the equation: $4x^4-ax^3+bx^2-cx+5=0$ knowing that they're all real, positives and that: $\frac{r_1}{2}+\frac{r_2}{4}+\frac{r_3}{5}+\frac{r_4}{8}=1$

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1985 OIM Problems/Problem 3

Problem

Solution