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

The zeros of a rational function are found by setting the function equal to zero and solving for $x$. For $g(x) = 5 + \frac{2}{x^2 + 5}$, setting $g(x) = 0$ yields no solution for $x$ because the fraction $\frac{2}{x^2 + 5}$ is always positive (since $x^2 + 5 > 0$ for all $x$), and adding 5 to a positive number cannot result in 0. Therefore, the function has no zeros.

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 $g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }$