Suppose $A$ be a $10\times 10$ order matrix and $a_{ii}=\alpha+1$ , $\alpha=?$

Question

Suppose $A=(a_{ij})$ be a $10\times 10$ order matrix such that $a_{ij}$=$1$ for $i\neq j$ and$ a_{ii}=\alpha+1$ for $\alpha\ge 0$.Let $ \lambda$ and $\mu $ be largest and smallest eigenvalues of $A$. If$\lambda+\mu=24$ then $\alpha=?$ here is my attempt -- according to the question diagonal elements are $\alpha+1$ and remaining entries are 1 then as sum of eigen value =sum of trace $10\alpha+10$=$\lambda+\mu+\sum_{i=2}^9\lambda_i $ suppose $\lambda_1=\mu$ and $\lambda_{10}=\lambda$ then $10\alpha$=$14+\sum_{i=2}^9\lambda_i $ as $\lambda+\mu=24$ but how can I find $\alpha$, is my process is correct? If not then what is the correct process?