This problem was contributed by @wrobel so we have to ask him. I guess it only refers to the quadratic form of the equation. The clue is to use the symmetry.What do you mean by quadrature? I can find several potential meanings that could be relevant. For example, it could mean doing an integral. It could mean a particular method of numerical solution. It could mean something about fitting things to a rectangle. It could mean something about a quadratic equation.