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Home » \[ \frac11 + 5\sqrt5-1 = -11 - 5\sqrt5 \] - jntua results

\[ \frac11 + 5\sqrt5-1 = -11 - 5\sqrt5 \] - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 By the **Remainder Theorem**, the remainder is simply $ f(1) $.

📌 f(1) = 1^3 + 2(1)^2 - 5(1) + 6 = 1 + 2 - 5 + 6 = 4.

📌 So the remainder is:

📌 f(x + 1) - f(x) = 6x + 4.

📌 Find $ f(x) $.

📌 This is a finite difference equation. Since the difference is linear in $ x $, $ f(x) $ must be a quadratic polynomial. Let:

📌 f(x) = ax^2 + bx + c.

📌 f(x + 1) = a(x + 1)^2 + b(x + 1) + c = a(x^2 + 2

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