\[x² - x - 2 = 0\]
\[x = 0 \Longrightarrow 0 - 2 = 0 \Longrightarrow\]
\[\Longrightarrow - 2 \neq 0 \Longrightarrow не\ корень.\]
\[x = \frac{1}{3} \Longrightarrow \frac{1}{9} - \frac{1}{3} - 2 = 0 \Longrightarrow\]
\[\Longrightarrow \frac{1 - 3}{9} - 2 \neq 0 \Longrightarrow не\ корень.\]
\[x = - 1 \Longrightarrow 1 + 1 - 2 = 0 \Longrightarrow\]
\[\Longrightarrow 0 = 0 \Longrightarrow корень.\]
\[x = - 0,5 \Longrightarrow \frac{1}{4} + \frac{1}{2} - 2 \neq 0 \Longrightarrow\]
\[\Longrightarrow не\ корень.\]
\[x = 2 \Longrightarrow 4 - 2 - 2 = 0 \Longrightarrow 0 =\]
\[= 0 \Longrightarrow корень.\]