Решебник по алгебре 9 класс Мерзляк Задание 365

\[\boxed{\text{365\ (365).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[y = ax^{2} + bx + 7\ \ \]

\[x = - 2 \rightarrow \ \ y = 0;\ \]

\[x = 3 \rightarrow \ \ y = 0.\]

\[\left\{ \begin{matrix} 4a - 2b + 7 = 0\ \ | \cdot 3 \\ 9a + 3b + 7 = 0\ \ \ |\ \cdot 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 12a - 6b + 21 = 0 \\ 18a + 6b + 14 = 0 \\ \end{matrix}\ \right.\ \ | +\]

\[30a + 35 = 0\]

\[a = - \frac{35}{30}\]

\[a = - \frac{7}{6}\]

\[- 4 \cdot \frac{7}{6} + b \cdot ( - 2) + 7 = 0\]

\[- \frac{14}{3} - 2b + 7 = 0\]

\[2b = \frac{21 - 14}{3}\]

\[2b = \frac{7}{3}\]

\[b = \frac{7}{6}\]

\[Ответ:\ a = - \frac{7}{6};\ \ b = \frac{7}{6}.\]