Question

a polynomial p(x) has a relative maximum at (-2,4), a relative minimum at (1,1), a relative maximum at (5,7) and no other critical points. how many zeros does p(x) have?
a one
b two
c three
d four
e five

Explanation:

Step1: Analyze the behavior of the polynomial

A polynomial changes its increasing - decreasing behavior at critical points. Here, the critical points are $x=-2,1,5$.

Step2: Consider the y - values of critical points

The relative maximum values are $y = 4$ at $x=-2$ and $y = 7$ at $x = 5$, and the relative minimum value is $y = 1$ at $x=1$. Since all $y$ - values of critical points are positive, the polynomial does not cross the $x$ - axis.

Answer:

A. One