# Root?

Algebra Level 3

Let the function $$f$$ be defined by $$f(x) = ke^x + x$$, where $$k$$ is a real number independent of $$x$$.

The intermediate value theorem shows that this function has at least one root in the interval $$]0,1[$$.

Which one of the following intervals can $$k$$ belong?

  

Clarification: $$e$$ denotes Euler's number, $$e \approx 2.71828$$.

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