On the coordinate plane, let $\Gamma$ denote the graph of the polynomial function $y = x ^ { 3 } - 4 x ^ { 2 } + 5 x$ , and let $L$ denote the line $y = m x$ , where $m$ is a real number. Based on the above, answer the following questions. (1) When $m = 2$ , find the $x$-coordinates of the three distinct intersection points of $\Gamma$ and $L$ in the range $x \geq 0$ . (2 points) (2) Based on (1), find the area of the bounded region enclosed by $\Gamma$ and $L$ . (4 points) (3) In the range $x \geq 0$ , if $\Gamma$ and $L$ have three distinct intersection points, then the maximum range of $m$ satisfying this condition is $a < m < b$ . Find the values of $a$ and $b$ . (6 points)
On the coordinate plane, let $\Gamma$ denote the graph of the polynomial function $y = x ^ { 3 } - 4 x ^ { 2 } + 5 x$ , and let $L$ denote the line $y = m x$ , where $m$ is a real number. Based on the above, answer the following questions.\\
(1) When $m = 2$ , find the $x$-coordinates of the three distinct intersection points of $\Gamma$ and $L$ in the range $x \geq 0$ . (2 points)\\
(2) Based on (1), find the area of the bounded region enclosed by $\Gamma$ and $L$ . (4 points)\\
(3) In the range $x \geq 0$ , if $\Gamma$ and $L$ have three distinct intersection points, then the maximum range of $m$ satisfying this condition is $a < m < b$ . Find the values of $a$ and $b$ . (6 points)