Let α, β be the two real roots of the equation x2 + px + q = 0, p, q ∈ R, q ≠ 0. If the quadratic equation g(x) = 0 has two real roots α + \(\frac{1}{\alpha}\), β + \(\frac{1}{\beta}\) such that sum of roots is equal to the product of roots, then the range of q is:
1
\(\left[\frac{1}{3}, 3\right]\)
2
\(\left[-\frac{1}{3}, 3\right]\)
3
\(\left[ -3, \frac{1}{3}\right]\)
4
\(\left[ -3, -\frac{1}{3}\right]\)