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If a continous founction of defined on the real line R, assumes positive and negative values in R, then the equation f(x)=0 has a root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum values is negative, then the equation `f(x)=0` has a root in R. Considetr `f(x)=ke^(x)-x` for all real x where k is real constant.
For `k gt 0,` the set of all values of k for which `ke^(x)-x=0` has two distinct, roots, is

A

`(0, 1//e)`

B

`(1//e, 1)`

C

`(1//e, oo)`

D

`(0,1)`

Text Solution

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The correct Answer is:
A
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