If a continous founction of defined on the real line R, assumes positive and negative val
Channel: Doubtnut
Date: 2019-12-29

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