Question

If f(x) is a third degree polynomial function , how many distinct complex roots are possible

Answer 1

the answer would be 0 or 2

Answer 2

Zero complex roots or two complex roots.

Explanation:

First of all, we have to know that complex roots can happen only in pairs, because they are based on the square root of a negative number.

On the other hand, a third degree polynomial can only have 3 roots as solution, because the degree of the polynomial specifies how many roots would have.

So, if we only can have 3 roots, and complex roots can only happen in pairs, then f(x) would have zero complex roots or two complex roots only, those are the unique scenarios.