Question

The graph of a rational function has local maxima at (-1,0) and (8,0). The complex number 2+3i is a zero of the function. What is the least possible degree of this function? (answer choices included)

a. 3
b. 4
c. 5
d. 6

Answer 1

Any polynomial's graph cannot have two simultaneous maxima, so they must contain a minima between them. Thus, the total number of turning points of the graph is 3. Generally, when plotting a polynomial, the number of turning points is:
n = d -1; where d is the degree of the polynomial and n is the number of turning points. Thus, this function's degree must be at least 4. The answer is b.

Answer 2

The answer is 6. That is what I got when I took the quiz