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Greatest Possible Coefficient Sum of Quartic Polynomial

Source:

August 8, 2024
algebrapolynomial2022

Problem Statement

If three of the roots of the quartic polynomial f(x)=x4+ax3+bx2+cx+df(x) = x^4 + ax^3 + bx^2 + cx + d are 00, 22, and 44, and the sum of aa, bb, and cc is at most 1212, then find the largest possible value of f(1)f(1).
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