Amazing Polynomial!

Algebra Level 5

The polynomial \(P(x) = x^3 + ax^2 + bx + c\) has the property that the mean of its zeros, the product of its zeros, and the sum of its coefficients are all equal. If the \(y\)-intercept of the graph of \(y = P(x)\) is 2, then what is the value of \(-b?\)

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