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📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 #### Yes, it is a right triangle.Question: A medical AI researcher models diagnostic accuracy using a polynomial $ p(x) $ such that $ p(1) = 3 $, $ p(2) = 10 $, $ p(3) = 21 $, and $ p(4) = 36 $. If $ p(x) $ is a cubic polynomial, find $ p(0) $.

📌 Solution: Let $ p(x) = ax^3 + bx^2 + cx + d $. We are given:

📌 p(1) &= a + b + c + d = 3, \\

📌 p(2) &= 8a + 4b + 2c + d = 10, \\

📌 p(3) &= 27a + 9b + 3c + d = 21, \\

📌 p(4) &= 64a + 16b + 4c + d = 36.

📌 We solve this system step by step. Subtract consecutive equations:

📌 Now subtract Eq 1 from Eq 2:

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