Let $f: R \rightarrow R$ be a twice differentiable function such that the quadratic equation $\mathrm{f}(\mathrm{x}) \mathrm{m}^{2}-2 \mathrm{f}^{\prime}(\mathrm{x}) \mathrm{m}+\mathrm{f}^{\prime}(\mathrm{x})=0$ in m , has two equal roots for every $\mathrm{x} \in \mathrm{R}$. If $\mathrm{f}(0)=1$, $\mathrm{f}^{\prime}(0)=2$ and $(\alpha, \beta)$ is the largest interval in which the function $f\left(\log _{e} x-x\right)$ is increasing, then $\alpha+\beta$ is equal to