Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .
A) $x = - \sqrt { 5 } , x = \sqrt { 5 }$
B)x = -4
C) $x = - \frac { 4 } { 5 } , x = \frac { 4 } { 5 }$
D)x = -5, x = 5
E)no zeros

Question

Quizplus · Accepted Answer

The zeros of a rational function are the values of $x$ for which the function equals zero. For $g(x) = 5 + \frac{4}{x^2 + 5}$, setting $g(x) = 0$ and solving for $x$ would involve finding an $x$ that makes $5 + \frac{4}{x^2 + 5} = 0$. However, since $x^2 + 5$ is always positive, the fraction $\frac{4}{x^2 + 5}$ is always positive, and adding 5 to a positive number cannot yield zero. Therefore, there are no values of $x$ that make $g(x) = 0$, meaning the function has no zeros.

Determine the Zeros (If Any) of the Rational Function g(x)=5+4x2+5g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }g(x)=5+x2+54​

Determine the Zeros (If Any) of the Rational Function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$