Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$ .
A)no zeros
B) $x = - \sqrt { 5 } , x = \sqrt { 5 }$
C) x = -5, x = 5
D) $x = - \frac { 6 } { 5 } , x = \frac { 6 } { 5 }$
E) x = -6

Question

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$ .
A)no zeros
B) $x = - \sqrt { 5 } , x = \sqrt { 5 }$
C) x = -5, x = 5
D)  $x = - \frac { 6 } { 5 } , x = \frac { 6 } { 5 }$
E) x = -6

Quizplus · Accepted Answer

To find the zeros of the function $g(x) = 5 + \frac{6}{x^2 + 5}$, we set $g(x) = 0$ and solve for $x$. However, because the fraction $\frac{6}{x^2 + 5}$ is always positive (since $x^2 + 5$ is always positive for all real $x$), and we are adding 5 to it, the function $g(x)$ will never equal zero. Therefore, the function has no zeros.

Determine the Zeros (If Any) of the Rational Function g(x)=5+6x2+5g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }g(x)=5+x2+56​

Determine the Zeros (If Any) of the Rational Function $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$