An algebra problem by mridul jain

Algebra Level 4

Let f ( x ) f(x) be a third-degree polynomial with real coefficients satisfying ∣ f ( 1 ) ∣ = ∣ f ( 2 ) ∣ = ∣ f ( 3 ) ∣ = ∣ f ( 5 ) ∣ = ∣ f ( 6 ) ∣ = ∣ f ( 7 ) ∣ = 12 |f(1)|=|f(2)|=|f(3)|=|f(5)|=|f(6)|=|f(7)|=12 . Find ∣ f ( 0 ) ∣ |f(0)| . '

This problem is from 2015 AIME.


The answer is 72.

Mridul Jain by mridul jain , 21, India

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1 solution

Sanjoy Kundu
Jun 12, 2020

Using recurrence relations, we see f(0) = f(1) + f(2) + ... + f(6) = 6*12 = 72.

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