I should say that I've never really try to "prove" many math theorems from my own point of view. Usually, I will just read through a proof and try to grasp the main concept. I stumbled upon this problem: Show that y = x3 - 3x + 6 only has one real root. It got me thinking that this can be generalized to a whole set of x3 functions will have only one real root as long as both of the min/max values are in the positive y of the graph. y' = 3x2 - 3 Min/max values: x = -1, 1 If I plug these values into the function I get: y(-1) = 8 y(1) = 4 Which are both positive. I then took the 2nd derivative to show that the concavity of both min/max values can only possibly go through the x-axis once. Which happens to be when x < -1. I'm lost on if that information was enough to "show that" for that particular problem. Furthermore, how can I begin generalizing this to a set of x3 equations? Thanks for any help.