# Get Conditions for Variable to be Real

I have a complex definition of a few variables (that I got using s = Solve[1 - a x^2 - x^3 == 0, x]) and I now want to know under what conditions of "a" will each of the solutions be real.

For example, one of the variables I have is r3=-(a/3) + ((1 - I Sqrt[3]) a^2)/( 3 2^(2/3) (-27 + 2 a^3 + 3 Sqrt[3] Sqrt[27 - 4 a^3])^( 1/3)) + ((1 + I Sqrt[3]) (-27 + 2 a^3 + 3 Sqrt[3] Sqrt[27 - 4 a^3])^(1/3))/(6 2^(1/3)), I want to know under what conditions will r3 be a real number.

I have tried simplifying this to the most basic example where I want to know what the conditions on a+b*I need to be so that it is real (where the answer I expect would be b=0), so I tried using Resolve[a + b I, Reals] but this does not give me the answer I expect.

You can just add a domain specification to Solve or NSolve:
NSolve[1 - a x^2 - x^3 == 0, x, Reals]