Разложите на множители квадратный трехчлен: 100c^2-50c+6.

Ответ:

\[100c² - 50c + 6 = 0\ \ \ \ \ |\ :2\]

\[50c^{2} - 25c + 3 = 0\]

\[\left\{ \begin{matrix} c_{1} + c_{2} = \frac{25}{50} = \frac{1}{2} \\ c_{1} \cdot c_{2} = \frac{3}{50}\text{\ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[c_{1} = \frac{3}{10};\ c_{2} = \frac{1}{5}:\]

\[\Longrightarrow 100c^{2} - 50c + 6 =\]

\[= 100 \cdot \left( c - \frac{3}{10} \right)\left( c - \frac{1}{5} \right) =\]

\[= (10c - 3)(10c - 2).\]