Determine the zeros of the function

The zero is x=2

Step-by-step explanation:

The zeros of the function are all those values for 'x' that makes f(x)=0, they are naturally located in the numerator of the function, but, sometimes denominator has something to say, so to find the zeros, its is important to perform factorization whenever we can and see if there terms that can be simplified.

x3 -8 is a cubed difference, hence, it can be written as (x-2)*(x2 +2x+4)

x3+8 is cub sum, hence, it can be written as = (x+2)*(x2-2x+2).

As you can see, no term can be simplified, therefore, the zeros of the function are located only in the cubed difference

(x-2)*(x2 +2x+4)=0

There are at least three options here

(x-2)=0, therefore x=2 is a zero.

(x2+2x+4)=0

But this expression needs the quadratic equation, and since it is a square root involved, we need to be sure that it can return real numbers and not complex using this expression:.

b2-4ac=4-4*1*4=-12

This means that we are going to have complex solutions, those are not zeros in real function.

Hence, our only zero is x=2

answer: 457.14

step-by-step explanation:

205 - 45 = 160

160 / .35 = 457.142857