\[\boxed{\text{280\ (280).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ Точка\ пересечения\ с\ \]
\[осью\ \text{Oy}\ (x = 0):\]
\[y = 0^{4} - 5 \cdot 0^{2} + 4 = 4 \Longrightarrow\]
\[\Longrightarrow точка\ \ (0;4).\]
\[Пересечение\ с\ осью\ \text{Ox\ }(y = 0):\]
\[x^{4} - 5x^{2} + 4 = 0\]
\[Пусть\ x^{2} = t;\ \ t \geq 0:\ \ \]
\[\ t^{2} - 5t + 4 = 0\]
\[t_{1} + t_{2} = 5;\ \ \ t_{1} \cdot t_{2} = 4\]
\[t_{1} = 1;\ \ \ t_{2} = 4\]
\[\left\{ \begin{matrix} x^{2} = 1 \\ x^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = \pm 1 \\ x = \pm 2 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow (1;0),\ ( - 1;0),\ ( - 2;0),\ (2;0);\]
\[\textbf{б)}\ Пересечение\ с\ осью\ \text{Oy}:\ \]
\[y = 0^{4} + 3 \cdot 0^{2} - 10 = - 10 \Longrightarrow\]
\[\Longrightarrow точка\ (0;\ - 10).\]
\[Пересечение\ с\ осью\ \text{Ox}:\]
\[x^{4} + 3x^{2} - 10 = 0\]
\[Пусть\ x^{2} = t;\ \ \ t \geq 0:\]
\[t^{2} + 3t - 10 = 0\]
\[D = 3^{2} + 4 \cdot 10 = 49\]
\[t_{1,2} = \frac{- 3 \pm 7}{2} = 2;\ - 5,\ \ \]
\[Так\ как\ t \geq 0,\ то:\]
\[x^{2} = 2\]
\[x = \pm \sqrt{2}\]
\[\Longrightarrow точки\ \left( - \sqrt{2};0 \right),\ \left( \sqrt{2};0 \right).\]
\[\textbf{в)}\ Пересечение\ с\ осью\ Oy:\]
\[y = 0^{4} - 20 \cdot 0^{2} + 100 =\]
\[= 100 \Longrightarrow точка\ (0;100).\]
\[Пересечение\ с\ осью\ \text{Ox}:\ \]
\[x^{4} - 20x^{2} + 100 = 0.\]
\[Пусть\ x^{2} = a;\ \ a \geq 0:\ \]
\[a^{2} - 20a + 100 = 0\]
\[(a - 10)^{2} = 0\]
\[a - 10 = 0\]
\[a = 10.\]
\[x^{2} = 10\ \ \]
\[x = \pm \sqrt{10}\]
\[\Longrightarrow точки\ \left( - \sqrt{10};0 \right),\ \left( \sqrt{10};0 \right).\]
\[\textbf{г)}\ Точка\ пересечения\ с\ \]
\[осью\ Oy:\]
\[y = 4 \cdot 0^{4} + 16 \cdot 0^{2} = 0 \Longrightarrow\]
\[\Longrightarrow точка\ (0;0).\]
\[Пересечение\ с\ осью\ Ox:\ \ \]
\[4x^{4} + 16x^{2} = 0\]
\[4x^{2}(x^{2} + 4) = 0\]
\[x = 0;\]
\[x^{2} = - 4 \Longrightarrow корней\ нет\]
\[\Longrightarrow (0;0).\]