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Roots of a Function

Source: 2014 AIME II #5

March 27, 2014

functionalgebrapolynomialquadraticsVietaemailAMC

Problem Statement

Real numbers

r

and

s

are roots of

p(x)=x^3+ax+b

, and

r+4

and

s-3

are roots of

q(x)=x^3+ax+b+240

. Find the sum of all possible values of

|b|

.

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