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Home » If \( n \equiv 1 \pmod3 \), then \( n^2 \equiv 1 \pmod3 \), - Veritas Home Health

If \( n \equiv 1 \pmod3 \), then \( n^2 \equiv 1 \pmod3 \), - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: Find the quadratic polynomial \( f(x) \) such that \( f(0) = 4 \), \( f(1) = 1 \), and \( f(2) = -4 \).

📌 Solution: Let \( f(x) = ax^2 + bx + c \). Use the given conditions:

📌 \( f(0) = c = 4 \)

📌 \( f(1) = a + b + c = 1 \) → \( a + b + 4 = 1 \) → \( a + b = -3 \)

📌 \( f(2) = 4a + 2b + c = -4 \) → \( 4a + 2b + 4 = -4 \) → \( 4a + 2b = -8 \) → \( 2a + b = -4 \)

📌 a + b = -3 \\

📌 2a + b = -4

📌 Subtract the first from the second: \( (2a + b) - (a + b) = -4 - (-3) \) → \( a = -1 \)

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