The question:

Show that the polynomial p, where has at least one real root.

I'm not sure what to do. Solving for 0 is difficult with a cubic, so I don't think this is the approach my text is looking for. This question is within some maxima-minima problems, so I'm thinking I need to use that train of thought. As far as I can tell, the derivative of p has no real roots, so I'm still stuck.

Any suggestions? Thanks.