If f(x) is a fifth degree polynomial, is it possible that it has exactly 5 complex roots? yes
no

No.

A fifth degree polynomial, having a graph that increases and starts from below x-axis.

Therefore, no matter what equation it is. The fifth degree polynomial will intercept x-axis AT LEAST one.

The fifth degree polynomial can have only at maximum, 4 complex roots.

You can try drawing or seeing the graph of fifth-degree polynomial function. No matter what equations, they still intercept at least one x-value.

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step-by-step explanation: