Let a, b, c be in arithmetic progression...

Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, e), (2, b) and (a, b) be `((10)/(3), 7/3)`. If `alpha, beta` are the roots of the equation `ax^2 + bx + 1 = 0`, then the value of `alpha^2 + beta^2 - alpha beta` is :

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