Cube Roots of Unity (Moulovibazar HS 2017)

Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm
Cube Roots of Unity (Moulovibazar HS 2017)

Unread post by samiul_samin » Tue Feb 20, 2018 5:10 pm

Let $f(x) =ax^2+bx+c$ ;($a,b,c\geq 0$).Given that,$f(p)×f(q)×f(r)=3abc-9$,where $p,q,r$ are complex cube-roots of unity.Find the minimum value of $abc$ which satisfies the given condition.(Here $abc$ means $a×b×c$)

Post Reply