I must find 3rd degree Polynomial functions in R[x] with:
1) no roots
2) only one root
3) only two roots
4) only 3 roots
If the function has a root, then prove it. If not, then explain why.
We know, that the cubic function can have one, two or three roots. But I really don't know, how I can find the polynomial functions.
A 3rd polynomial function can not have no root because a polynomial function have at least one root. (Continous function)