Let p be the sum of all possible determinates of order 2 having 0,1,2 and 3 as their four elements.
Then the common root  $\text{'}\alpha \text{'}$  of the equations  $x^2+ax+[m+1]=0,x^2+bx+[m+4]=0$, ${\alpha }^2-cx+[m+15]=0$ , such that   $\alpha >p$ , where  $a+b+c=0$  and  $m=\underset{n\to \infty }{\lim }\frac{1}{n}\sum _{r=1}^{2n}\frac{r}{\sqrt{n^2+r^2}}$ (Where  $[.]$ denotes the greater integer function)