I think that the point of this exercise is to show by means of examples that when the discriminant test is inconclusive almost anything can happen.

The function in (a) can be written as . It's obvious from that that the (global) minimum value of this function is 0, and that this minimum value occurs at the origin (and also at all the points on the lines ).

To see what happens in (b), notice that the function is zero along the curves and . Then think about what happens to the function on the coordinate axes and also on the curve .