Let and let be given by

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

a\in\mathbb{R}

and let

f:\mathbb{R}\to\mathbb{R}

be given by

f(x)=x^5-5x+a

. Then, (1)

f(x)

has three real roots if

a>4

. (2)

f(x)

has only one real root if

a>4

. (3)

f(x)

has three real roots if

a<-4

. (4)

f(x)

has three real roots if

-4<a<4