Each angle is 180(p-2)/p.
180-{360}/{p} = k
So 360/p has to be an integer.
360 = 2^3 * 3^2 * 5^1
So there are 4 * 3 * 2 = 24 possibilities, but we exclude 1 and 2, because p > = 3
So , 24 -2 = 22
Hence, choice (c) is the right answer
General term - nCr * (x^2)^(n-r) (3y)^r
It is given that 2n - 2r + r = 52n - r = 5n = 4 => r = 3
So the term we have here is 4C3 * (x^2)^1 (3y)^3Coefficient = 4C3 * 3^3 = 4 * 27 = 108
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
