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

For a rational function to have zeros, the numerator must be equal to zero. In this case, the numerator is a constant (5) and does not depend on $x$, meaning it cannot be made zero by any value of $x$. Therefore, the function $g(x) = 5 + \frac{6}{x^2 + 5}$ 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 $g ( x ) = 5 + \frac { 6 } { x ^ { 2 } + 5 }$