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Home » Ratio of complex burrows = 3/8 - Red Crowns

Ratio of complex burrows = 3/8 - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \frac{a^2}{a^2} = \boxed{1}

📌 Question: A polynomial $ f(x) $ satisfies $ f(x + 1) - f(x) = 6x + 4 $. Find the leading coefficient of $ f(x) $.

📌 Solution: Since the difference $ f(x+1) - f(x) $ is linear, $ f(x) $ must be a quadratic polynomial. Let $ f(x) = ax^2 + bx + c $. Then:

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

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

📌 f(x+1) - f(x) = 6x + 4

📌 2a = 6 \Rightarrow a = 3, \quad a + b = 4 \Rightarrow 3 + b = 4 \Rightarrow b = 1

📌 Thus, the leading coefficient of $ f(x) $ is $ \boxed{3} $.

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