Find the zeros (if any) of the rational function. (If there are no zeros, enter NONE.)

Question

g(x) = (x^3-64)/(x^2+2)

need help solving

Answer 1

A fraction can only be zero if its numerator is zero
so
x^3 - 64 = 0
difference of cube factoring ....
(x-4)(x^2 + 4x + 16) = 0
x = 4 or x = (-4 ± √(16- 64) )/2
x = 4 or x = -2 ± 4√3 i

so the graph should cross the x-axis only once, at x = 4

confirmation:

http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x%5E3-64%29%2F%28x%5E2%2B2%29+for+x+%3D++-20+to+20