\[\boxed{\text{731\ (731).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ y = x² + 15\]
\[y \in \lbrack 15; + \infty).\]
\[\textbf{б)}\ y = (x - 16)²\]
\[y \in \lbrack 0; + \infty).\]
\[\textbf{в)}\ y = - x^{2} + 8\]
\[y \in ( - \infty;8\rbrack.\]
\[\boxed{\text{731.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[Квадратное\ уравнение\ \]
\[не\ имеет\ корней,\ когда\ \]
\[D < 0\ или\ \]
\[D = b^{2} - 4ac < 0.\]
\[\textbf{а)}\ kx² + 8x - 15 = 0\]
\[D = 8^{2} + 4 \cdot 15 \cdot k = 64 + 60k,\]
\[64 + 60k < 0\]
\[k < - \frac{64}{60}\]
\[k < - \frac{16}{15} < - 1\frac{1}{15}.\]
\[Ответ:при\ k < - 1\frac{1}{15}.\]
\[\textbf{б)}\ 6x² - 3x + k = 0\]
\[D = 3^{2} - 4 \cdot 6 \cdot k = 9 - 24k,\]
\[9 - 24k < 0\]
\[8k > 3\]
\[k > \frac{3}{8}.\]
\[Ответ:при\ k > \frac{3}{8}.\]
\[\textbf{в)}\ 5x² + kx + 1 = 0\]
\[D = k^{2} - 4 \cdot 5 \cdot 1 = k^{2} - 20,\]
\[k^{2} - 20 < 0\]
\[k^{2} < 20\]
\[Ответ:при\ \ \ - 2\sqrt{5} < k < 2\sqrt{5}.\]
\[\textbf{г)}\ 7x² - kx - 1 = 0\]
\[D = k^{2} + 4 \cdot 7 \cdot 1 = k^{2} + 28,\]
\[k^{2} + 28 < 0\]
\[k² < - 28 \Longrightarrow ни\ при\ каком\ k.\]
\[Ответ:нет\ таких\ k.\]