Inspired by Calvin Lin

Algebra Level 5

If the polynomial f(x)=4x4a.x3+b.x2c.x+5f(x)=4x^4-a.x^3+b.x^2-c.x+5 where a,b,cRa,b,c \in \mathbb{R} has 44 positive real zeroes(roots) say r1,r2,r3, and r4r_1,r_2,r_3, \ and \ r_4, such that r12+r24+r35+r48=1\frac{r_1}{2}+\frac{r_2}{4}+\frac{r_3}{5}+\frac{r_4}{8}=1 Find the value of aa.

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