For $k0$, the set of all values of $k$ for which $k e^x-x=0$ has two distinct roots is\

Question

For $k>0$, the set of all values of $k$ for which $k e^x-x=0$ has two distinct roots is\

Professor PC Thomas Classes · Answer

(a) : For 2 distinct roots of\ $f(x)=k e^{x}-x, f(x)_{\min }<0$\ $\Rightarrow 1+\ln k<0$ or $0<k<\frac{1}{e}$\ $	herefore \quad k \in\left(0, \frac{1}{e}ight)$\