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