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Let a in R and let f: R to R be given b...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
D
`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`.
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