Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 1 } { x ^ { 2 } + 5 }$.
A) $x = - 1 , x = 1$
B) $x = 1$
C) $x = - \sqrt { 5 } , x = \sqrt { 5 } , x = 1$
D) $x = - \sqrt { 5 } , x = \sqrt { 5 } , x = - 1 , x = 1$
E) no zeros

Question

Quizplus · Accepted Answer

The zeros of the rational function $g(x) = \frac{x^3 - 1}{x^2 + 5}$ are found by setting the numerator equal to zero and solving for $x$. The equation $x^3 - 1 = 0$ simplifies to $x^3 = 1$, which has the solution $x = 1$. The denominator $x^2 + 5$ does not affect the zeros since it cannot be zero (it's always positive). Therefore, the only zero of the function is $x = 1$.

Determine the Zeros (If Any) of the Rational Function g(x)=x3−1x2+5g ( x ) = \frac { x ^ { 3 } - 1 } { x ^ { 2 } + 5 }g(x)=x2+5x3−1​

Determine the Zeros (If Any) of the Rational Function $g ( x ) = \frac { x ^ { 3 } - 1 } { x ^ { 2 } + 5 }$