Find the zeros (if any) of the rational function.
$f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$
A)-2
B)2
C)8
D)-8
E)None

Question

Find the zeros (if any) of the rational function. 
 $f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$  
A)-2
B)2
C)8
D)-8
E)None

Quizplus · Accepted Answer

To find the zeros of the function, we set $f(x) = 0$ and solve for $x$. Thus, we have $0 = 2 + \frac{12}{x^2 + 2}$. This equation implies that the fraction $\frac{12}{x^2 + 2}$ must be equal to -2 for the equation to hold. However, since $x^2 + 2$ is always positive for all real numbers $x$, the fraction $\frac{12}{x^2 + 2}$ can never be negative. Therefore, there are no real values of $x$ that satisfy the equation, meaning the function has no zeros.

Find the Zeros (If Any) of the Rational Function f(x)=2+12x2+2f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }f(x)=2+x2+212​

Find the Zeros (If Any) of the Rational Function $f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$