Descartes Rule of Sign
x cubed has a positive sign, x squared negative, x negative, and 5 positive.
+ - - +
1 sign change from + to - and then another from - to +.
We have 2 sign changes.
Positive solutions are 2 or 0. You always have two choices from greater than or equal to 2.
(+) 2 or 0
Now make x negative.
- - + +
We have 1 sign change from - to +.
Therefore, (-) 1. We don't subtract 2 since, 1 or -1 solutions isn't possible. Only 1 is.
Since we had 2 or 0 positive, we must have 2 or 0 imaginary. This is because we know we have 1 negative and if there are 0 positive, we must have 2 imaginary.