Let $0 < x _ { 1 } < x _ { 2 }$. A function f defined on the set of real numbers as $$f ( x ) = \left( x - x _ { 1 } \right) \left( x - x _ { 2 } \right)$$ The parabola represented by this function intersects the axes at different points A and B in the rectangular coordinate plane as shown in the figure. The distances from points A and B to the origin are equal, and this parabola takes its minimum value when $x = \frac { 3 } { 5 }$. Accordingly, what is the ratio $\frac { \mathbf { x } _ { \mathbf { 2 } } } { \mathbf { x } _ { \mathbf { 1 } } }$? A) 2 B) 3 C) 4 D) 5 E) 6
Let $0 < x _ { 1 } < x _ { 2 }$. A function f defined on the set of real numbers as
$$f ( x ) = \left( x - x _ { 1 } \right) \left( x - x _ { 2 } \right)$$
The parabola represented by this function intersects the axes at different points A and B in the rectangular coordinate plane as shown in the figure.
The distances from points A and B to the origin are equal, and this parabola takes its minimum value when $x = \frac { 3 } { 5 }$. Accordingly, what is the ratio $\frac { \mathbf { x } _ { \mathbf { 2 } } } { \mathbf { x } _ { \mathbf { 1 } } }$?\\
A) 2\\
B) 3\\
C) 4\\
D) 5\\
E) 6