Question

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

Answer 1

the answer should be letter b

Answer 2

Correct option is:

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

Explanation:

The roots of a polynomial function p(x) lies in an interval (a,b) if:

p(a)>0 and p(b)<0

or

p(a)<0 and p(b)>0

Here,

f(2.5)>0 and f(3.0)<0

Hence, f(x) has a root between 2.5 and 3.0

Also, f(4.5)>0 and f(4.0)<0

Hence, f(x) has a root between 4.0 and 4.5

Hence, Correct option is:

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