JEE-Advanced 2014 (1/40)

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 $-4<a<4$ .