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Home » Multiply numerator and denominator by the conjugate of the denominator \(2 + \sqrt5\): - Network4

Multiply numerator and denominator by the conjugate of the denominator \(2 + \sqrt5\): - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 #### 3,375,000**Question: A herpetologist studying reptile population dynamics models the growth of a lizard population with a quadratic polynomial \( h(x) \) such that \( h(0) = 3 \), \( h(1) = 8 \), and \( h(2) = 15 \). Find \( h(x^2 + 2) \).

📌 To find the quadratic polynomial \( h(x) = ax^2 + bx + c \), we use the given conditions:

📌 \( h(0) = 3 \) implies \( c = 3 \).

📌 \( h(1) = 8 \) gives us \( a(1)^2 + b(1) + 3 = 8 \) which simplifies to \( a + b + 3 = 8 \). Thus, \( a + b = 5 \).

📌 \( h(2) = 15 \) gives us \( a(2)^2 + b(2) + 3 = 15 \) which simplifies to \( 4a + 2b + 3 = 15 \). Thus, \( 4a + 2b = 12 \).

📌 Now, solve the system of equations:

📌 \( a + b = 5 \)

📌 \( 4a + 2b = 12 \)

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