Determine the zeros (if any) of the rational function $g ( x ) = 7 + \frac { 3 } { x ^ { 2 } + 7 }$.
A) $\quad x = - \sqrt { 7 } , x = \sqrt { 7 }$
B) $x = - 3$
C) $x = - \frac { 3 } { 7 } , x = \frac { 3 } { 7 }$
D) $x = - 7 , x = 7$
E) no zeros

Question

Quizplus · Accepted Answer

The function $g(x) = 7 + \frac{3}{x^2 + 7}$ does not have any zeros because the fraction $\frac{3}{x^2 + 7}$ is always positive (since $x^2 + 7 > 0$ for all real numbers $x$), and adding 7 to a positive number cannot result in 0.

Determine the Zeros (If Any) of the Rational Function g(x)=7+3x2+7g ( x ) = 7 + \frac { 3 } { x ^ { 2 } + 7 }g(x)=7+x2+73​

Determine the Zeros (If Any) of the Rational Function $g ( x ) = 7 + \frac { 3 } { x ^ { 2 } + 7 }$