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 function are the solutions to $x^3 - 1 = 0$. Factoring this as $(x - 1)(x^2 + x + 1) = 0$, we find that $x = 1$ is the only real solution, making B the correct choice. The denominator $x^2 + 5$ does not affect the zeros since it cannot be zero (it's always positive).

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 $g ( x ) = \frac { x ^ { 3 } - 1 } { x ^ { 2 } + 5 }$