Решите уравнение: x^3+5x^2+7x+2=0.

\[x³ + 5x² + 7x + 2 = 0\]

\[P( - 2) =\]

\[= ( - 2)^{3} + 5 \bullet ( - 2)^{2} + 7 \bullet ( - 2) + 2 =\]

\[= - 8 + 20 - 14 + 2 = 0\]

\[(x + 2)\left( x^{2} + 3x + 1 \right) = 0\]

\[x + 2 = 0\]

\[x = - 2.\]

\[x^{2} + 3x + 1 = 0\]

\[D = 3^{2} - 4 \bullet 1 \bullet 1 = 9 - 4 = 5\]

\[x_{1} = \frac{- 3 + \sqrt{5}}{2};\ \ \ \ x_{2} = \frac{- 3 - \sqrt{5}}{2}\]

\[Ответ:\ - 2;\ \ \frac{- 3 + \sqrt{5}}{2};\ \]

\[\ \frac{- 3 - \sqrt{5}}{2}.\]