X | f (x)

2.0 | 2.8

2.5 | 1.1

3.0 | - 0.8

3.5 | - 1.2

4.0 | - 0.3

4.5 | 0.7

For the given table of values for a polynomial function, where must the zeros of the function lie?

A. between 2.0 and 2.5 and between 4.0 and 4.5

B. between 2.5 and 3.0 and between 4.0 and 4.5

C. between 2.0 and 2.5 and between 3.5 and 4.0

D. between 2.5 and 3.0 and between 3.5 and 4.0

Option B.

Step-by-step explanation:

If the value of function is 0 at x=c, then c is a root or zero of the function. It means the graph of function intersect x-axis at its zeroes.

From the given table it is clear that the value of function are

x | f (x) | Sign

2.0 | 2.8 | Positive

2.5 | 1.1 | Positive

3.0 | - 0.8 | Negative

3.5 | - 1.2 | Negative

4.0 | - 0.3 | Negative

4.5 | 0.7 | Positive

The sign of values of function changes in interval 2.5-3.0 and 4.0-4.5.

It means, the graph of function must intersect x-axis in interval 2.5-3.0 and 4.0-4.5. So, the zeros of the function lie between 2.5 and 3.0 and between 4.0 and 4.5.

Therefore, the correct option is B.