Parellelograms and polynomials together, Really?

The lengths of the sides of a triangle $ABC$ with centroid at $G$ are the roots of the

cubic polynomial:

$k(x)=x^3-25x^2+200x-500$

If $P, Q$ and $R$ are the points in the plane of the triangle such that

$PAGB, QBGC$ and $RAGC$ are parallelograms. Then find the value of:

$PG^2+QG^2+RG^2$