Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 2 }$.
A) $x = 2$
B) $x = \frac { 3 } { 2 } , x = - \frac { 3 } { 2 }$
C) $x = - 9 , x = 9$
D) $x = - 3 , x = 3$
E) no zeros

Question

Quizplus · Accepted Answer

To find zeros of the function, we need to set the numerator equal to zero and solve for $x$. $x^2-9 = 0$ has solutions $x = -3$ and $x=3$. Notice that $x=2$ is not a valid zero, since it would make the denominator equal to zero which is undefined for a rational function. Therefore, the answer is choice D.

Determine the Zeros (If Any) of the Rational Function f(x)=x2−9x−2f ( x ) = \frac { x ^ { 2 } - 9 } { x - 2 }f(x)=x−2x2−9​

Determine the Zeros (If Any) of the Rational Function $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 2 }$