Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices ( a, c ),(2, b ) and ( a, b ) be (10/3, 7/3). If α, β are…

Let $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c}$ be in arithmetic progression. Let the centroid of the triangle with vertices $\displaystyle (\mathrm{a}, \mathrm{c}),(2, \mathrm{~b})$ and $\displaystyle (\mathrm{a}, \mathrm{b})$ be $\displaystyle \left(\frac{10}{3}, \frac{7}{3}\right)$. If $\displaystyle \alpha, \beta$ are the roots of the equation $\displaystyle \mathrm{a} x^2+\mathrm{b} x+1=0$, then the value of $\displaystyle \alpha^2+\beta^2-\alpha \beta$ is :