ГДЗ по алгебре и начала математического анализа 10 класс Колягин Задание 130

\[\boxed{\mathbf{130}.}\]

\[1)\ ax^{2} + 5x = 0\]

\[x(ax + 5) = 0\]

\[x = 0;\ \ \ ax + 5 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ax = - 5\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{5}{a}.\]

\[2)\ ax^{2} - 3x = 0\]

\[x(ax - 3) = 0\]

\[x = 0;\ \ \ \ ax - 3 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ax = 3\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{3}{a}.\]

\[3)\ x^{2} - a = 0\]

\[x^{2} = a\]

\[x = \pm \sqrt{a};\ \ если\ a \geq 0.\]

\[нет\ корней,\ если\ a < 0.\]

\[4)\ 2x^{2} + a = 0\]

\[2x^{2} = - a\]

\[x^{2} = - \frac{a}{2}\]

\[нет\ корней,\ если\ a > 0;\]

\[x = 0;если\ a = 0;\]

\[x = \pm \sqrt{\frac{a}{2}};если\ a < 0.\]