I have a math problem that maybe someone could help me with. The question is: What type of roots does -5x^3 + 10x^2=6x. (^ means to the power of). I need to know if it has real roots, complex roots, or both and how many of each.
It has one real root : 0 and the other two roots it has are complex so two of those. Since it is degree of 3 it will have to have at least three roots if not more, but in this case it only has three. If you got a graphing calculator like the TI-83 or what not you can use the program under APPS called PolySmlt and from there use the first program number 1. (Poly Root Finder) TYpe in the highest degree that something is to in this case it would be 3. Then put in -5 for the a3, 10 for the a2, and then -6 for the a1 since if you move the 6 over to the left side it becomes negative. since you don't have a number that is not to a degree put a zero in for a0. This program will only show you real roots so if it says nonreal you will have to use the Quadratice equation to find the other ones.
The other roots should be -10+i√(20)/-10

And -10-i√(20)/-10