The roots are a and b:
a + b = p and ab = 12
(a + b)^2 = p^2
(a - b)^2 = (a + b)^2 - 4ab
=> (a - b)^2 = p^2 - 12 * 4 = p^2 - 48
If |a - b| ≥ 12 { Difference between the roots is at least 12}
then, (a - b)^2 ≥ 144
p^2 - 48 ≥ 144
p^2 ≥ 192
P ≥ 8√3 or P ≤ -8√3