the roots of the equations $\left|\begin{array}{ccccc}{.}^x{C}_r& & {.}^{n-1}{C}_r& & {.}^{n-1}{C}_{r-1}\\ {.}^{x+1}{C}_r& & {.}^n{C}_r& & {.}^n{C}_{r-1}\\ {.}^{x+2}{C}_r& & {.}^{n+1}{C}_r& & {.}^{n+1}{C}_{r-1}\end{array}\right|=0$

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