Now the goal is to get one line tangent to the parabola. Lets try them both. Lets graph it to check. Now, add the graph of the product and then test it to see if the curves are tangent. That looks good.
Lets zoom in at the roots.
This seems to be a useful direction. We have the following graph. Zoom in for a closer look. Summary Many issues are hidden in these composite accounts of examination of this problem. Each senario presents a somewhat different approach.