Let  $f\left(x\right)=2023x^n+a_{n-1}{x}^{n-1}+a_{n-2}{x}^{n-2}+\mathrm{......}+a_{1}x+a_0,\forall a_i\in ℝ,0\le i\le n-1$
Let ${\alpha }_1,{\alpha }_2,\mathrm{.......}{\alpha }_n$ be n roots such that  $\prod _{i=2}^n({\alpha }_1-{\alpha }_i)=M,(M\in ℝ-\left\{0\right\})$
If $L=\underset{x\to {\alpha }_1}{\lim }{\left(1+f\left(x\right)\right)}^{{ }^{\left[\frac{1}{x-{\alpha }_1}\right]}}$ where ${\alpha }_1$ is a real root and the value of $\frac{{\log }_{e}L}{{\rm M}}$ is a four digit number abcd, then a + b – c + d is equal to

$$\begin{gathered} f\left(x\right)=2023x^n+a_{n-1}{x}^{n-1}+\mathrm{......}+a_{1}x+a_0\forall a_i\in ℝ \\ \Rightarrow f\left(x\right)=2023(x-{\alpha }_1)(x-{\alpha }_2)\mathrm{.........}(x-{\alpha }_n) \\ L=\underset{ }{\underset{x\to {\alpha }_1}{\lim }}{[1+2023\prod _{i=1}^n(x-{\alpha }_i)]}^{\frac{2023{\displaystyle \prod _{i=2}^n(x-{\alpha }_i)}}{2023{\displaystyle \prod _{i=1}^n(x-{\alpha }_i)}}} \\ Since, 2023\prod _{i=1}^n(x-{\alpha }_i)=t \\ L=\underset{ }{\underset{x\to {\alpha }_1}{\lim }}{\left[{(1+t)}^{\frac{1}{t}}\right]}^{2023\prod _{i=2}^n(x-{\alpha }_i)} \\ L=e^{\underset{x\to {\alpha }_1}{\lim },\frac{2023{\displaystyle \prod _{i=2}^n(x-{\alpha }_i)}}{t}(1+t-1)} \\ \Rightarrow L=e^{2023M} \\ \Rightarrow Lo{g}_{e}L=2023M \end{gathered}$$

$\frac{Lo{g}_{e}L}{M}=2023$ so in the form of four digit number abcd therefore 

$a+b-c+d = 3$