•First of all, I counted the turning points. There are two, so that means this polynomial function has THREE roots. (# of turning points+1=number of roots.)
•Next, look to see how many times the function crosses the x-axis. This is the number of REAL solutions. In this case, there is one point at which the f(x) is crossing the x-axis so there is one real solution.
•Since there is one real solution there has to be 2 imaginary roots. (Total # of solutions-real solutions=imaginary solutions)
NOTE: the turning points are where the increasing intervals change to decreasing and the decreasing change to increasing. The first derivative at these points is 0.
