Question

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

Answer 1

Answer:

(B). between 2.5 and 3.0 and between 4.0 and 4.5.

Step-by-step explanation:

According to the Question,

• If the value of the function is 0 at x=c, then c is a root or zero of the function. It means the graph of function intersects the 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 the x-axis in intervals 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.