Answer: \(x^2 - 7x + 12 = 0\)
Let the roots be \(\alpha\) and \(\beta\). Then \(\alpha + \beta = 7\) and \(\alpha^3 + \beta^3 = 91\).
\(\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)\)
\(91 = 7^3 - 3\alpha\beta(7) = 343 - 21\alpha\beta\)
\(21\alpha\beta = 343 - 91 = 252\), so \(\alpha\beta = 12\).
The equation is \(x^2 - (\alpha + \beta)x + \alpha\beta = 0\), i.e. \(x^2 - 7x + 12 = 0\).
(The roots are 3 and 4: \(3 + 4 = 7\) and \(27 + 64 = 91\) ✓.)