From Larson's "Problem Solving Through Problems" 7.2.10:
Given that $f(x) :=x^6-6x^5+ax^4+bx^3+cx^2+dx+1$ has its roots as all positive, find $a,b,c,d$
Thus chapter is about (generalized) Arithmetic-geometric mean inequality so I would have to use that. I believe it's implied from the problem that all roots are real.
Any hints or solution would be great.