Use a similar strategy as in your other question, [19925664].
3x² + 4x + 12 = 3 (x - r ) (x - s)
3x² + 4x + 12 = 3 (x² - (r + s) x + rs)
3x² + 4x + 12 = 3x² - 3 (r + s) x + 3rs
so that
r + s = -4/3
rs = 12/3 = 4
Recall that
(r + s)² = r² + 2rs + s²
so that
r² + s² = -2rs = -2(4) = -8
