Consider The three functions no longer intersect at 1 on the y-axis. Lets graph and see. In this process we seem to have also noticed that the lines and the parabola intersect at the points when the lines cross the x-axis. 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.