Let a `in R` and let f: `R to R` be given by f(x) `=x^(5) -5x+a.` then

Options

A. `f(x)` has three real roots if `agt4`
B. `f(x)` has only one real root fi `agt4`
C. `f(x)` has three real roots if `alg-4`
D. `f(x)` has three real roots, if `-4ltalt4`

Answer

D

Explanation

`f(x)=x^(5)-5x` and `g(x)=-a`
`:.f'(x)=5x^(4)-5`

`=5(x^(2)+1)(x-1)(x+1)`
Clearly `f(x)=g()` has one real root, if `a gt4` and three real roots if `|a|lt4`.