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
Correct Answer: P ≥ 8
√ 3
or P ≤
-8
√ 3