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📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Now use $ a + b + c + d = 3 $:

📌 -\frac{5}{3} + 15 - \frac{112}{3} + d = 3 \Rightarrow \left( -\frac{117}{3} + 15 \right) + d = 3 \Rightarrow -39 + 15 + d = 3 \Rightarrow d = 27

📌 So $ f(0) = d = \boxed{27} $

📌 Question: A computational biologist is analyzing a genetic model where the number of possible gene expression patterns corresponds to the product of the roots of the equation

📌 x\sqrt{x} - 7x + 10\sqrt{x} = 0.

📌 Find this product.

📌 Solution: Let $ \sqrt{x} = y $, so $ x = y^2 $. Substituting gives:

📌 y^2 \cdot y - 7y^2 + 10y = 0 \Rightarrow y^3 - 7y^2 + 10y = 0 \Rightarrow y(y^2 - 7y + 10) = 0

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