AIME 2010 II #7 — Cubic P(z)=z³+az²+bz+c Roots w+3i w+9i 2w-4

2175ExpertPolynomialsComplex NumbersAlgebra

AIME II · 2010 · Problem 7

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 $|a+b+c|$.

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AIME 2010 II #7 — Cubic P(z)=z³+az²+bz+c Roots w+3i w+9i 2w-4

2175ExpertPolynomialsComplex NumbersAlgebra

AIME II · 2010 · Problem 7

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 $|a+b+c|$.

0 students attempted0% solvedRating 2175