Not Your Average Average

Algebra Level pending

Consider three distinct complex numbers \( \alpha, \beta \) and \( \gamma \) that yield the same value when substituted as \( x \) in the polynomial \(p(x) = x^3 - 2x^2 + 4x - 8 \).

Evaluate the average of the expression \( \alpha + \beta \gamma \) throughout all its possible values.

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