Need Help finding answer

Question

Find the zeros (if any) of the rational function. Show all work.

Answer 1

Since your notation is a little vague, I am assuming you have provided the rational function f(x)=2+(12/(x^2=2)).

To solve, you will first set this equation equal to zero and then try and isolate or solve for the x variable as follows:

2+(12/(x^2+2))=0

(12/(x^2+2))=-2

12/(-2)=(x^2+2)) (The denominator and numerator switch places so that you can isolate the variable.)

-6=x^2+2

x^2=-8

x=+/-sqrt(-8) --> No Real Solution

Since you cannot evaluate the square root of a negative number, there will be no real solutions. If you are dealing with imaginary numbers or complex numbers, then you can break down the square root of -8 by prime factorization to get +/-2i(sqrt2) (plus or minus two "i" square root of two).