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

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- January 8th 2011, 02:32 AMjacksNo. of real roots.
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 - January 8th 2011, 07:11 AMsnowtea
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? - January 8th 2011, 07:12 PMjacks