Решите уравнение: x^3+3x^2+4x+4=0.

\[x³ + 3x² + 4x + 4 = 0\]

\[P( - 2) =\]

\[= ( - 2)^{3} + 3 \bullet ( - 2)^{2} + 4 \bullet ( - 2) + 4 =\]

\[= - 8 + 12 - 8 + 4 = 0\]

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

\[x + 2 = 0\]

\[x = - 2.\]

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

\[D = 1^{2} - 4 \bullet 1 \bullet 2 = 1 - 8 =\]

\[= - 7 < 0 \Longrightarrow нет\ решения.\]

\[Ответ:\ - 2.\]