MathDB

Let P(z) \equal{} z^3 \plus{} az^2 \plus{} bz \plus{} c, where

a

b

, and

c

are real. There exists a complex number

w

such that the three roots of

P(z)

are w \plus{} 3i, w \plus{} 9i, and 2w \minus{} 4, where i^2 \equal{} \minus{} 1. Find |a \plus{} b \plus{} c|.

Problem Statement