The question can be re-phrased as: "Under what circumstances are L and V exactly constant for every point in the scene as seen through every pixel on the image plane? Under what circumstances are they approximately constant?" (Incorporated into posted assignment, 10:00am, 6/3/09.)
he start of the question can be re-phrased as: "Let's take the approach of simply assuming L and V are constant for every point in the scene as seen through every pixel in the image plane -- regardless of whether this assumption is satisfied under the actual lighting and viewing conditions -- and use the halfway vector for specular shading." (Incorporated into posted assignment, 10:00am, 6/3/09.)
The drawings corresponds to the case of z ~= -1.5, as shown on the previous page. However, you do not need to compute any roots. You should be able to draw rays that correspond to various root situations, as suggested in the fourth bullet under the discussion of roots as well as the lecture slides about ray-sphere intersection.
NOTE: For problem 2b, you should assume that the ray origin is located somewhere outside the bounding box of the object. (Incorporated into posted assignment, 10:00am, 6/3/09.)