Mathematics

Problem

Let

a

b

c

be in arithmetic progression. Let the centroid of the triangle with vertices

(a, c)

(2, b)

and

(a, b)

\left(\frac{10}{3}, \frac{7}{3}\right)

. 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 (a)

-\frac{71}{256}

(b)

\frac{71}{256}

(c)

-\frac{69}{256}

(d)

\frac{69}{256}