I try to prove that toplological space on the real plane with the zariski toplogy is not a Hausdorff space. I tried to prove it by claiming that the intersection of two opens U=V(A)^c and W=V(B)^c with A and B subsets of R[X,Y] is infiniteand thus also the intersection between U and W is finite. But not every polynomial has finitely many zero points, such as p(x,y) = xy +y^2. How can I proove this more rigorously?