Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$ .
A) $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 4$
B)no zeros
C) x = -4, x = 4
D) x = 4
E) $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 4 , x = 4$

Question

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$ .
A) $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 4$
B)no zeros
C) x = -4, x = 4
D) x = 4
E)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 4 , x = 4$

Quizplus · Accepted Answer

The zeros of the function are found by setting the numerator equal to zero and solving for x. The numerator $x^3 - 64$ can be factored as $(x - 4)(x^2 + 4x + 16)$, which equals zero when $x = 4$. The denominator does not affect the zeros of the function.

Determine the Zeros (If Any) of the Rational Function g(x)=x3−64x2+6g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }g(x)=x2+6x3−64​

Determine the Zeros (If Any) of the Rational Function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$