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Relive the Joy – This Smiling Dog Meme is Spreading Like Wildfire! - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Thus, the critical points are:

📌 oxed{1 + rac{\sqrt{3}}{3}, 1 - rac{\sqrt{3}}{3}}

📌 Question:** A quantum machine learning algorithm designer models the probability amplitude for a quantum state transition with the function \( p(x) = x^4 - 4x^3 + 6x^2 - 4x + 1 \). Verify if \( x = 1 \) is a root of multiplicity greater than 1.

📌 Solution:** To verify if \( x = 1 \) is a root of multiplicity greater than 1 for \( p(x) = x^4 - 4x^3 + 6x^2 - 4x + 1 \), we first check if \( p(1) = 0 \).

📌 Calculate \( p(1) \):

📌 p(1) = 1^4 - 4 imes 1^3 + 6 imes 1^2 - 4 imes 1 + 1 = 1 - 4 + 6 - 4 + 1 = 0

📌 Since \( p(1) = 0 \), \( x = 1 \) is indeed a root. To check the multiplicity, we compute the derivative \( p'(x) \):

📌 p'(x) = 4x^3 - 12x^2 + 12x - 4

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