Determine the zeros (if any) of the rational function $g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }$ .
A)x = -6, x = 6
B) $x = - \sqrt { 6 } , x = \sqrt { 6 }$
C) $x = - \frac { 1 } { 2 } , x = \frac { 1 } { 2 }$
D)x = -3
E)no zeros

Question

Quizplus · Accepted Answer

To find the zeros of the function $g(x) = 6 + \frac{3}{x^2 + 6}$, we set $g(x) = 0$ and solve for $x$. However, the equation $0 = 6 + \frac{3}{x^2 + 6}$ has no solution because the fraction $\frac{3}{x^2 + 6}$ is always positive (since $x^2 + 6 > 0$ for all $x$), and adding 6 to a positive number cannot result in 0. Therefore, the function has no zeros.

Determine the Zeros (If Any) of the Rational Function g(x)=6+3x2+6g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }g(x)=6+x2+63​

Determine the Zeros (If Any) of the Rational Function $g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }$