# Careful with basics

Algebra Level 3

Let $$P(x)$$ be a polynomial of degree $$3$$ with real coefficients. Which of the following is possible?

A: $$P(x)$$ has no real roots.

B: $$P(x)$$ has exactly $$2$$ real roots, and they are distinct numbers.

C: $$P(1) = -1$$, $$P(2) = 1$$, $$P(3) = 11$$ and $$P(4) = 35$$.

D: $$i - 2017$$ and $$i + 2017$$ are the roots of $$P(x)$$.

Clarification: $$i=\sqrt{-1}$$ denotes the imaginary unit.

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