Algebra Level 3

If $a\in \mathbb R$ and $f:\mathbb R \to \mathbb R$ is 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.

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