2007 AMC 12A Problem 18

Since $f$ has real coefficients, the conjugates $-2i$ and $2-i$ are also roots. Thus $$\begin{gathered} f(x) = (x^2+4)(x^2-4x+5) \\ = x^4-4x^3+9x^2 \\ {}-16x+20. \end{gathered}$$ Then $a+b+c+d=-4+9$ $-16+20$ $=9.$ Equivalently, $a+b+c+d=f(1)-1$ $=(1+4)(1+1)-1$ $=9.$ Thus, the correct answer is D.