Решите систему неравенств: 3x+9<0; 2x^2+5x+2>=0.

Ответ:

\[\left\{ \begin{matrix} 3x + 9 < 0\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x^{2} + 5x + 2 \geq 0 \\ \end{matrix} \right.\ \]

\[2x^{2} + 5x + 2 = 2(x + 2)(x + 0,5)\]

\[D = 25 - 16 = 9\]

\[x_{1} = \frac{- 5 + 3}{4} = - \frac{2}{4} = - 0,5;\]

\[x_{2} = \frac{- 5 - 3}{4} = - 2.\]

\[\left\{ \begin{matrix} 3x < - 9\text{\ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 2(x + 2)(x + 0,5) \geq 0 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x < - 3\ \ \ \\ x \leq - 2\ \ \ \\ x \geq - 0,5 \\ \end{matrix} \right.\ \]

\[x < - 3.\]

\[Ответ:x < - 3.\]