Решите уравнение: x^3+2x^2-x+6=0.

\[x³ + 2x² - x + 6 = 0\]

\[P( - 3) =\]

\[= ( - 3)^{3} + 2 \bullet ( - 3)^{2} - ( - 3) + 6 =\]

\[= - 27 + 18 + 3 + 6 = 0\]

\[(x + 3)\left( x^{2} - x + 2 \right) = 0\]

\[x + 3 = 0\]

\[x = - 3.\]

\[x^{2} - x + 2 = 0\]

\[D = ( - 1)^{2} - 4 \bullet 1 \bullet 2 =\]

\[= 1 - 8 = - 7 < 0 \Longrightarrow\]

\[\Longrightarrow нет\ решения.\]

\[Ответ:\ - 3.\]