Find all the real zeros of the following polynomial. \[ f(x)=x^{4}-729 x \] Enter your answer(s) as ordered pairs, \( (x, y) \). They are already separated by pomma. Provide your answer below:

To find the real zeros of the polynomial \( f(x) = x^{4} - 729x \), we start by setting the function equal to zero: \[ x^{4} - 729x = 0 \] Factoring out \( x \): \[ x(x^{3} - 729) = 0 \] This gives us one solution directly: \[ x = 0 \] Now, to find the other solutions, we solve \( x^{3} - 729 = 0 \): \[ x^{3} = 729 \] Taking the cube root of both sides, we find: \[ x = 9 \] Now, we also need to check for complex roots. The cubic equation can also yield complex solutions, but since we are interested in real zeros only, we can stop here. Thus, the real zeros we found are \( x = 0 \) and \( x = 9 \). The ordered pairs representing these zeros are: \[ (0, 0), (9, 0) \]