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Home » Using Vieta's formulas, the sum and product of the roots are given by: - Portal da AcÃºstica

Using Vieta's formulas, the sum and product of the roots are given by: - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \mathbb{E}[\text{output}] = \sum_{k=0}^{3} (8 - k) \cdot \frac{\binom{8}{k}}{256} + \sum_{k=4}^{8} k \cdot \frac{\binom{8}{k}}{256}

📌 Compute each sum.

📌 First sum ($k = 0$ to $3$):

📌 $ (8-0)\binom{8}{0} = 8 \cdot 1 = 8 $

📌 $ (8-1)\binom{8}{1} = 7 \cdot 8 = 56 $

📌 $ (8-2)\binom{8}{2} = 6 \cdot 28 = 168 $

📌 $ (8-3)\binom{8}{3} = 5 \cdot 56 = 280 $

📌 Total = $8 + 56 + 168 + 280 = 512$

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