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Home » Flame Grant Me Strength: Unlock Mind-Blowing Power Over Adversity! - Sterling Industries

Flame Grant Me Strength: Unlock Mind-Blowing Power Over Adversity! - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 2Question: Let $ f(x) $ be a cubic polynomial such that $ f(1) = 5, $ $ f(2) = -3, $ $ f(3) = 11, $ and $ f(4) = 45. $ Find $ f(0). $

📌 Now use equation (1): $ a + b + c + d = 5 $

📌 Since the divisor is quadratic, the remainder is linear: $ R(x) = ax + b $. Then:

📌 f(a + b + c) = f(a) + f(b) + f(c) - 3f(abc)

📌 We now know $ f(a + b) = f(a) + f(b) $ for all $ a,b $. So $ f $ is additive.

📌 Now return to original equation (since $ f(0) = 0 $ and additivity is known):

📌 But $ f(a + b + c) = f(a) + f(b) + f(c) $, so:

📌 So the only solution is the zero function.

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