Question

For what values of c does the equation 3 x^2 + 12x + c = 0 have 1 real root, 2 real roots, and 2 non-real roots?

Answer 1

1 real root: c=12
2 real roots: c<12
2 non-real roots: c>12

Answer 2

The determinant from the quadratic formula is useful here. b^2-4ac