Question

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

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.