Consider the quadratic equation \( (n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0,\, n\in R \). Let \( \alpha \) be the minimum value of the product of its roots and \( \beta \) be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is \( \alpha \) and the common ratio is \( \dfrac{\alpha}{\beta} \), is:
