\[\boxed{\text{533\ (533).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ 2x^{2} + 3x + 1 = 0\]
\[D = b^{2} - 4ac = 3^{2} - 4 \cdot 2 \cdot 1 =\]
\[= 9 - 8 = 1\]
\[D > 0 - 2\ корня.\]
\[\textbf{б)}\ 2x^{2} + x + 2 = 0\]
\[D = b^{2} - 4ac = 1^{2} - 4 \cdot 2 \cdot 2 =\]
\[= 1 - 16 = - 15\]
\[D < 0 - корней\ нет.\]
\[\textbf{в)}\ 9x^{2} + 6x + 1 = 0\]
\[D = b^{2} - 4ac = 6^{2} - 4 \cdot 9 \cdot 1 =\]
\[= 36 - 36 = 0\]
\[D = 0 - один\ корень.\]
\[\textbf{г)}\ x^{2} + 5x - 6 = 0\]
\[D = b^{2} - 4ac =\]
\[= 5^{2} - 4 \cdot 1 \cdot ( - 6) = 25 + 24 =\]
\[= 49\]
\[D > 0 - два\ корня.\ \]