Eisatopon Math AI Challenges: Problem of the Week: 2010 AIME II, Problem 7

Δευτέρα 10 Απριλίου 2017

Let $P(z)=z^3+az^2+bz+c$ , where a, b, and c are real. There exists a complex number $w$ such that the three roots of

$P(z)$ are $w+3i$ , $w+9i$ , and $2w-4$ , where $i^2=-1$ . Find $|a+b+c|$ .