Answer: \(x^2 - 5x + 6 = 0\)
\(\alpha + \beta = 5\), \(\alpha^3 + \beta^3 = 35\).
\[\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)\]\[35 = 125 - 15\alpha\beta\]\[\alpha\beta = 6\]Equation: \(x^2 - 5x + 6 = 0\) (roots 2 and 3; check \(8 + 27 = 35\)).