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A quadratic function \( f(x) = ax^2 + bx + c \) has roots at \( x = 2 \) and \( x = -3 \). If \( f(1) = 6 \), find the value of \( a \).
Since the roots are 2 and -3, the function can be written as \( f(x) = a(x - 2)(x + 3) \).
Expanding, \( f(x) = a(x^2 + x - 6) \).

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