If $x^6-12x^5+ax^4+bx^3+cx^2+dx+64=0$ has positive roots then find $a,b,c,d$.
I did something but that don't deserve to be added here, but what I thought before doing that is following:
- For us, Product and Sum of roots are given.
- Roots are positive.
- Hence I tried to use AM-GM-HM inequalities, as sum and product are given, but I failed to conclude something good.
So please deliver some hints or solution regarding AM-GM-HM inequalities.