Question

Which is a ppssible number of distinct real roots for a cubic function select all that apply.

0
1
3
4

Answer 1

Try graphing y=x^3. It crosses the x-axis at (0,0), and this point represents the one and only real root.

Every form of a cubic function has a graph that crosses the x-axis in 1 or 3 places.

Thus, the correct answers to this particular problem are B and C.

Additionally, certain cubic function forms have graphs that cross the x-axis in one unique place, but which touch (but do not cross) the x-axis. Here you have one unique real root plus one repeated (duplicated) real root, for a total of 3 roots.

Using these facts, decide which of the four given answers are correct.