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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