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 \(-4<a<4\).

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