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