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Let \( a, b, c \) be in arithmetic progression. Let the centroid of the triangle with vertices \( (a, c),(2, b) \) and \( (a, b) \)
P be \( \left(\frac{10}{3}, \frac{7}{3}\right) \). If \( \alpha, \beta \) are the roots of the equation \( a x^{2}+b x \)
W) \( +1=0 \), then the value of \( \alpha^{2}+\beta^{2}-\alpha \beta \) is:
[JEE Main-2021 (February)]
(a) \( \frac{71}{256} \)
(b) \( -\frac{69}{256} \)
(c) \( \frac{69}{256} \)
(d) \( -\frac{71}{256} \)
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