Algebra Level 4

Let $$a\in \mathbb R$$ and let $$f:\mathbb R \to \mathbb R$$ be given by $$f(x)=x^5-5x+a$$, then which of the followings is/are true?

(A) $$f(x)$$ has three real roots if $$a>4$$.

(B) $$f(x)$$ has only one real root if $$a>4$$.

(C) $$f(x)$$ has three real roots if $$a<-4$$.

(D) $$f(x)$$ has three real roots if $$-4<a<4$$.

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