JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

Let $A\left(\alpha, \frac{1}{\alpha}\right) B\left(\beta, \frac{1}{\beta}\right)$ and $C\left(\gamma, \frac{1}{\gamma}\right)$ be the vertices of a $\triangle A B C$, where $\alpha, \beta$ are the roots of the equation $x^2-6 p_1 x+2=0$ and $\beta, \gamma$ are the roots of the equation $x^2-6 p_2 x+3=0$ and $\gamma, \alpha$ are the roots of the equation $x^2-6 p_3 x+6=0, p_1, p_2, p_3$ being positive. Then, the coordinates of the centroid of $\triangle A B C$ are