If a continuous $f$ 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 $R$. Consider $f(x)=k e^x-x$ for all real $x$ where $k$ is a real constant.
The line $\mathrm{y}=\mathrm{x}$ meets $\mathrm{y}=\mathrm{ke}^{\mathrm{x}}$ for $\mathrm{k} \leq 0$ at