Quant Boosters  Rajesh Balasubramanian  Set 5

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  48If a  b ≥ 12 { Difference between the roots is at least 12}
then, (a  b)^2 ≥ 144p^2  48 ≥ 144
p^2 ≥ 192
P ≥ 8√3 or P ≤ 8√3