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

Question

Quizplus · Accepted Answer

To determine the zeros of a function, we want to find the values of x that make the function equal to zero. However, in this case, there is no way to simplify the expression to make it equal to zero. Therefore, there are no zeros for this rational function. Instead, this function has vertical asymptotes at x = sqrt(7) and x = -sqrt(7) because the denominator becomes zero at those points.

Determine the Zeros (If Any) of the Rational Function g(x)=7+2x2+7g ( x ) = 7 + \frac { 2 } { x ^ { 2 } + 7 }g(x)=7+x2+72​

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