Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }$.
A) $x = - \sqrt { 5 } , x = \sqrt { 5 }$
B) $x = - 2$
C) $x = - \frac { 2 } { 5 } , x = \frac { 2 } { 5 }$
D) $x = - 5 , x = 5$
E) no zeros

Question

Quizplus · Accepted Answer

Zeros of a rational function are the values of $x$ that make the numerator of the rational function equal to zero. However, in this case, the numerator is simply a constant term of 5, so it can never be zero. Therefore, the rational function has no zeros. Option $\boxed{	extbf{(E)}}$ is the correct answer.

Determine the Zeros (If Any) of the Rational Function g(x)=5+2x2+5g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }g(x)=5+x2+52​

Determine the Zeros (If Any) of the Rational Function $g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }$