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Home » Thus, the conic is **not degenerate**. - Esdistancia

Thus, the conic is not degenerate. - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 Question: A science communicator is designing an interactive exhibit on symmetry and defines a function \( h(x) = x^3 + px + q \) to model visual patterns. If \( h(1) = 4 \), \( h(2) = 10 \), and \( h(3) = 24 \), find the value of \( h(0) \).

📌 Solution: We are given a cubic polynomial \( h(x) = x^3 + px + q \), and values:

📌 h(1) = 1^3 + p(1) + q = 1 + p + q = 4 \quad ext{(1)}

📌 h(2) = 8 + 2p + q = 10 \quad ext{(2)}

📌 h(3) = 27 + 3p + q = 24 \quad ext{(3)}

📌 p + q = 3 \quad ext{(i)}

📌 2p + q = 2 \quad ext{(ii)}

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