f(x) = a(x - 2)(x + 3)
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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:
- 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:
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