A well-characterized approximation problem

The authors consider the following NP optimization problem: given a set of polynomials P_i(x), i=1. . .s of degree at most 2 over GF[p] in n variables, find a root common to as many as possible of the polynomials P_i(x). They prove that in the case when the polynomials do not contain any squares as monomials, it is always possible to approximate this problem within a factor of ^p2 /_p-1 in polynomial time. This follows from the stronger statement that one can, in polynomial time, find an assignment that satisfies at least ^p-1/_p2 of the nontrivial equations. More interestingly, they prove that approximating the maximal number of polynomials with a common root to within a factor of p-∈ is NP-hard. They also prove that for any constant δ<1, it is NP-hard to approximate the solution of quadratic equations over the rational numbers, or over the reals, within n^δ