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Home » The Most Iconic Pokémon Protagonists That Defined Generations of Gamers! - Redraw

The Most Iconic Pokémon Protagonists That Defined Generations of Gamers! - Redraw

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 So $ g(x) $ has roots at $ x = 1, 2, 3, 4 $. But $ g(x) $ is a cubic polynomial, while a cubic polynomial cannot have 4 distinct roots unless it is identically zero — contradiction.

📌 Therefore, such a cubic polynomial cannot exist — unless the values force a special form. But the values $ f(1)=10, f(2)=20, f(3)=30, f(4)=40 $ suggest $ f(x) - 10x $ has four zeros. So define:

📌 Then $ g(1) = g(2) = g(3) = g(4) = 0 $. So $ g(x) $ has roots at $ 1,2,3,4 $, so $ g(x) = k(x-1)(x-2)(x-3)(x-4) $, but this is degree 4 — contradiction, since $ f(x) $ is cubic.

📌 Unless — the only way this is possible is if $ g(x) $ is not degree 4 — but it must be degree 4 unless $ f(x) $ is not truly cubic. But the problem says it is cubic.

📌 So the only resolution is that our assumption of cubicity is violated — but the problem states it. Hence, no such cubic exists — but that cant be, as the problem asks for $ f(5) $.

📌 Ah — perhaps we must use finite differences.

📌 But the problem says $ f(x) $ is cubic. So either the problem is flawed or we misinterpret. But perhaps cubic includes constant leading coeff? No — degree exactly 3.

📌 Unless $ f(x) - 10x $ has four zeros — impossible for degree 3. So the only way the conditions hold is if $ f(x) = 10x $, and accept its not truly cubic — but the problem states it is.

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