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

Correct option is:

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

Step-by-step 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

step-by-step explanation:

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225