Conjugate Pairs in Polynomials

by First, Jan 6, 2017, 12:56 AM

2010 AIME II #7 wrote:
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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wait barn, you are given the roots of a polynomial and asked for $|P(1)-1|$ :P

by FlyingCucumber, Jan 11, 2017, 12:03 AM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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