JEE Math Practice Question

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

1. A.$${{69} \over {256}}$$
2. B.$${{71} \over {256}}$$
3. C.$$ - {{71} \over {256}}$$
4. D.$$ - {{69} \over {256}}$$