\[(p - 1)x^{2} + (p - 1)x - 1 = 0\ \ \ \ \]
\[при\ \ \ D = 0\]
\[D = (p - 1)^{2} + 4 \cdot (p - 1) = 0\]
\[p^{2} - 2p + 1 + 4p + 4 = 0\]
\[p^{2} + 2p - 3 = 0\]
\[D = 4 + 12 = 16\]
\[p = \frac{- 2 \pm 4}{2}\]
\[p_{1} = 1;\ \ \ \ \ p_{2} = - 3\]
\[Ответ:\ \ при\ p = 1;p = - 3.\ \]