Let be a polynomial of degree , an odd positive integer, and has monotonic behaviour , then the number of real roots of the equation
is equal to
I think the point is that is monotonic means that is monotonic in the same direction (increasing/decreasing).
The sum of of monotonic functions in the same direction is monotonic.
How many real roots can a monotonic function have?
E.g. how many times can a strictly increasing function intersect the x-axis?