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Zeros of Quadratic Function with Coefficient Sum Zero

Very Hard Advanced Math Quadratic Equations

Consider the quadratic function defined by the equation:

$$f(x) = ax^2 + bx + c$$

where $a$, $b$, and $c$ are real numbers. If the function has zeros at $x = 2$ and $x = -3$, and if the sum of the coefficients $a$, $b$, and $c$ equals $0$, find the value of $a$. Express your answer as both a decimal and a fraction.

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