A problem in Quadratic equations

The condition that x^4 + a.(x^3) + b.(x^2) + c.x + d is a perfect square is
A) c^2 = a.d
B) c^2 = a.(d^2)
C) c^2 = (a.d)^2
D) c^2 = d.(a^2)

the answer is D...... BUT HOW!!!???

x⁴ + ax³ +bx² + cx + d = (x²+mx+n)²

Expand the RHS

x⁴ + ax³ +bx² + cx + d = x⁴ + m²x² + n² + 2nx² + 2mx³ + 2mnx

x⁴ + ax³ +bx² + cx + d = x⁴ +2mx³ + (m²+2n)x² + 2mnx+ n²

Matching the coefficients on both sides you get

a = 2m
b = m²+2n
c = 2mn
d= n²

So
c² = (2m)²n² = da²