1. Problem: Given a parabola defined by the function $$f(x) = (x - x_1)(x - x_2)$$ with roots $$0 < x_1 < x_2$$, the parabola intersects the coordinate axes at points A and B such that the distances from the origin to A and B are equal. 2. The parabola has its minimum value at $$x = \frac{3}{5}$$. 3. We need to find the ratio $$\frac{x_2}{x_1}$$. 4. Since $$f(x) = (x - x_1)(x - x_2) = x^2 - (x_1 + x_2)x + x_1 x_2$$, the vertex (minimum point) of the parabola is at $$x = \frac{x_1 + x_2}{2}$$. 5. Given the vertex is at $$x = \frac{3}{5}$$, we have: $$\frac{x_1 + x_2}{2} = \frac{3}{5} \implies x_1 + x_2 = \frac{6}{5}$$ 6. Points A and B are the x-intercepts at $$x_1$$ and $$x_2$$, so their coordinates are $$A = (x_1, 0)$$ and $$B = (x_2, 0)$$. 7. The parabola also intersects the y-axis at $$x=0$$, so the y-intercept is: $$f(0) = (0 - x_1)(0 - x_2) = x_1 x_2$$ 8. The points A and B have distances from the origin equal, so: $$|OA| = |OB| \implies |x_1| = |x_2|$$ But since $$0 < x_1 < x_2$$, the points A and B are on the x-axis at positive values, so the distances are simply $$x_1$$ and $$x_2$$. This contradicts the problem statement that distances from origin to A and B are equal, so the other point must be the y-intercept. 9. The problem states the parabola intersects the axes at points A and B, and their distances from the origin are equal. So one point is on the x-axis at $$x_1$$ or $$x_2$$, the other is on the y-axis at $$f(0) = x_1 x_2$$. Therefore, the distances are: $$|OA| = x_1$$ (assuming A is at $$(x_1,0)$$) $$|OB| = |x_1 x_2|$$ (assuming B is at $$(0, x_1 x_2)$$) Given $$|OA| = |OB|$$, we have: $$x_1 = x_1 x_2 \implies x_2 = 1$$ 10. Using $$x_1 + x_2 = \frac{6}{5}$$ and $$x_2 = 1$$, we get: $$x_1 + 1 = \frac{6}{5} \implies x_1 = \frac{6}{5} - 1 = \frac{1}{5}$$ 11. Finally, the ratio is: $$\frac{x_2}{x_1} = \frac{1}{\frac{1}{5}} = 5$$ Answer: D) 5