ГДЗ по алгебре 9 класс Макарычев Задание 214

\[\boxed{\text{214\ (214).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[Чтобы\ найти\ корни\ \]

\[многочлена,\ приравняем\ \]

\[его\ к\ нулю\ и\ решим\]

\[квадратное\ уравнение.\]

\[\textbf{а)}\ \frac{1}{6}x^{2} + \frac{2}{3}x - 2 = 0\ \ \ \ | \cdot 6\]

\[x^{2} + 4x - 12 = 0\]

\[D_{1} = 2^{2} + 12 = 4 + 12 = 16\]

\[x_{1} = - 2 - 4 = - 6;\ \ \ \ x_{2} =\]

\[= - 2 + 4 = 2.\]

\[Ответ:x = - 6;\ \ x = 2.\]

\[\textbf{б)}\ \frac{1}{2}x^{2} - \frac{1}{3}x - \frac{1}{4} = 0\ \ \ \ | \cdot 12\]

\[6x^{2} - 4x - 3 = 0\]

\[D_{1} = 2^{2} + 3 \cdot 6 = 4 + 18 = 22\]

\[x_{1,2} = \frac{2 \pm \sqrt{22}}{6}\]

\[Ответ:x = \frac{2 \pm \sqrt{22}}{6}.\]

\[\textbf{в)} - x^{2} + 4x - 2\frac{3}{4} = 0\]

\[x^{2} - 4x + \frac{11}{4} = 0\ \ \ \ \ \ \ | \cdot 4\]

\[4x^{2} - 16x + 11 = 0\]

\[D_{1} = 8^{2} - 4 \cdot 11 = 64 - 44 = 20\]

\[x_{1,2} = \frac{8 \pm \sqrt{20}}{4} = \frac{4 \pm \sqrt{5}}{2}.\]

\[Ответ:x = \frac{4 \pm \sqrt{5}}{2}.\]

\[\textbf{г)}\ 0,4x^{2} - x + 0,2 = 0\ \ \ \ \ \ | \cdot 5\]

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

\[D = 25 - 4 \cdot 2 = 25 - 8 = 17\]

\[x = \frac{5 \pm \sqrt{17}}{4}.\]

\[Ответ:x = \frac{5 \pm \sqrt{17}}{4}.\]