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Home » r² = 4² = 16. - Abu Waleed Tea

r² = 4² = 16. - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 & & 1 & 1 & -2 \\

📌 & 1 & 1 & -2 & 0 \\

📌 So $ R(x) = (x - 1)(x^2 + x - 2) $. Factor the quadratic:

📌 x^2 + x - 2 = (x + 2)(x - 1).

📌 R(x) = (x - 1)^2(x + 2).

📌 The roots are $ x = 1 $ (with multiplicity 2) and $ x = -2 $. Therefore, there are **two distinct real roots**, but **three real roots counting multiplicity**. Since the question asks for the number of real roots (not distinct), the answer is:

📌 Question: A zoologist studying social behavior models the interaction between two animals with the function $ I(u) = u - \frac{u^3}{9} $. If $ n $ is a positive integer, define $ x_n $ as the value of $ u $ such that $ I(x_n) = \frac{1}{n} $. Find $ \lim_{n \to \infty} x_n $.

📌 Solution: We are given $ I(u) = u - \frac{u^3}{9} $, and $ I(x_n) = \frac{1}{n} $. So:

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