Решебник по алгебре 9 класс Мерзляк Задание 226

\[\boxed{\text{226\ (226).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[f(x) = - 2x^{2} + 5x\]

\[1)\ f(1) = - 2 \cdot 1 + 5 = 3\]

\[f(0) = 0\]

\[f\left( \frac{1}{2} \right) = - 2 \cdot \frac{1}{4} + 5 \cdot \frac{1}{2} =\]

\[= - \frac{1}{2} + \frac{5}{2} = \frac{4}{2} = 2\]

\[f( - 5) = - 2 \cdot 25 - 25 =\]

\[= - 50 - 25 = - 75\]

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

\[- x \cdot (2x - 5) = 0\]

\[\left\{ \begin{matrix} x = 0\ \ \ \ \ \ \ \ \ \\ 2x - 5 = 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 0\ \ \ \\ x = 2,5 \\ \end{matrix} \right.\ \]

\[Ответ:x = 0;x = 2,5.\]

\[- 2x^{2} + 5x = 2\]

\[- 2x^{2} + 5x - 2 = 0\]

\[D = 25 - 16 = 9\]

\[x = \frac{- 5 + 3}{- 4} = \frac{- 2}{- 4} = \frac{1}{2}\]

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

\[\left\{ \begin{matrix} x = \frac{1}{2} \\ x = 2 \\ \end{matrix} \right.\ \]

\[Ответ:x = 2;x = 0,5.\]

\[- 2x^{2} + 5x = - 3\]

\[- 2x^{2} + 5x + 3 = 0\]

\[D = 25 + 24 = 49\]

\[x = \frac{- 5 + 7}{- 4} = - \frac{1}{2}\]

\[x = \frac{- 5 - 7}{- 4} = 3\]

\[\left\{ \begin{matrix} x = - \frac{1}{2} \\ x = 3\ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:\ x = - 0,5;x = 3.\]

\[3)\ а)\ f( - 1) = 7 - неверно:\]

\[f( - 1) = - 2 \cdot 1 - 5 = - 7\]

\[- 7 \neq 7.\]

\[\textbf{б)}\ f(4) = - 12 - верно:\]

\[f(4) = - 2 \cdot 16 + 5 \cdot 4 =\]

\[= - 32 + 20 = - 12\ \]

\[- 12 = - 12.\ \]