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Absolute Value of Third-Degree Polynomial is 12

Source: 2015 AIME I Problem 10

March 20, 2015

absolute valuealgebrapolynomialAMCAIMEAIME I

Problem Statement

Let

f(x)

be a third-degree polynomial with real coefficients satisfying

|f(1)|=|f(2)|=|f(3)|=|f(5)|=|f(6)|=|f(7)|=12.

Find

|f(0)|