Let a   ∈ R and let f   : R → R be given by f x = x 5 - 5 x + a , then

1. $f\left(x\right)$ has three real roots if $a>4$
2. $f\left(x\right)$ has only one real roots if $a>4$
3. $f\left(x\right)$ has three real roots if $a< -4$
4. $f\left(x\right)$ has three real roots if $-4<a<4$

Solution

Asked in: JEE Advanced 2014 (Paper 1)

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