# Parellelograms and polynomials together, Really?

Geometry Level 5

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:

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

×