\[\boxed{\text{1059.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[Имеет\ 2\ корня,\ при\ D > 0.\]
\[x^{2} - 4ax + 4a^{2} - 25 = 0,\]
\[\ \ a = 1,\ \ b = - 4a,\ \ \]
\[c = 4a^{2} - 25\]
\[D = ( - 4a)^{2} - 4 \cdot 1 \cdot\]
\[\cdot \left( 4a^{2} - 25 \right) = 16a^{2} - 16a^{2} +\]
\[+ 100 = 100\]
\[x_{1,2} = \frac{4a \pm 10}{2} = 2a \pm 5\]
\[\left\{ \begin{matrix} 2a + 5 > 2 \\ 2a - 5 > 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} 2a > - 3 \\ 2a > 7\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} a > - 1,5 \\ a > 3,5\ \ \ \\ \end{matrix} \right.\ \Longrightarrow \ \ a \in (3,5;\ + \infty)\]
\[Ответ:при\ a \in (3,5;\ + \infty).\]