\begin{array} { l } { \text { If } 1 - p \text { is a root of quadratic equation } } { x ^ { 2 } + p x + ( 1 - p ) = 0 \text { , then the roots are } } \end{array}

Substitute x = 1 - p into the quadratic equation x^2 + px + (1 - p) = 0. This gives (1 - p)^2 + p(1 - p) + (1 - p) = 0, which factors to (1 - p)(1 - p + p + 1) = 0. Solving this yields (1 - p)(2) = 0, meaning p = 1. Substituting p = 1 back into the original equation gives x^2 + x = 0, which factors as x(x + 1) = 0, resulting in the roots 0 and -1.

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