It is given that

\(\alpha + \beta + \gamma = 3, \quad \alpha^2 + \beta^2 + \gamma^2 = 5, \quad \alpha^3 + \beta^3 + \gamma^3 = 6.\)

The cubic equation \(x^3 + bx^2 + cx + d = 0\) has roots \(\alpha, \beta, \gamma\).

Find the values of \(b, c\) and \(d\).