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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question:** An angel investor is evaluating a startup's growth model, represented by the cubic polynomial \( f(t) = t^3 + pt^2 + qt + r \), where \( t \) is time in years. If \( f(0) = 2 \), \( f(1) = 0 \), and \( f(2) = -2 \), find the coefficients \( p \), \( q \), and \( r \).

📌 Solution:** We know the cubic polynomial \( f(t) = t^3 + pt^2 + qt + r \) satisfies:

📌 \( f(0) = 2 \) implies \( r = 2 \).

📌 \( f(1) = 0 \) implies \( 1 + p + q + r = 0 \).

📌 \( f(2) = -2 \) implies \( 8 + 4p + 2q + r = -2 \).

📌 Substitute \( r = 2 \) into the equations:

📌 From \( f(1) = 0 \):

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