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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 F(2) = \frac{100 \cdot 2}{2^2 + 4} = \frac{200}{8} = 25.

📌 Question: A meteorologist studying rainfall patterns defines a function $ R(x) = x^3 - 3x + 2 $. How many real roots does $ R(x) $ have?

📌 Solution: We analyze the cubic polynomial $ R(x) = x^3 - 3x + 2 $. To find the number of real roots, we first attempt rational root theorem: possible rational roots are $ \pm1, \pm2 $. Testing:

📌 R(1) = 1 - 3 + 2 = 0 \Rightarrow x = 1 \text{ is a root}.

📌 Divide $ R(x) $ by $ x - 1 $ using synthetic division:

📌 \begin{array}{r|rrrr}

📌 & 1 & 0 & -3 & 2 \\

📌 & & 1 & 1 & -2 \\

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