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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 #### 19.47

📌 The function \( f(x) = ax^2 + bx + c \) has roots at \( x = 2 \) and \( x = -3 \). If \( f(1) = 6 \), find the value of \( a \).

📌 The function can be expressed in factored form based on the roots:

📌 f(x) = a(x - 2)(x + 3)

📌 Expand the expression:

📌 f(x) = a(x^2 + 3x - 2x - 6) = a(x^2 + x - 6)

📌 Substitute \( x = 1 \) into the expanded form and set it equal to 6:

📌 f(1) = a(1^2 + 1 - 6) = 6

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