Problem:
What is the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions and , each with leading coefficient
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Solution:
The -coordinates of the intersection points are precisely the zeros of the polynomial . This polynomial has degree at most three, so it has at most three zeros. Hence, the graphs of the fourth degree polynomial functions intersect at most three times. Finding an example to show that three intersection points can be achieved is left to the reader.