The binomial expansion of $$\[ (3+k x)^{-2} \quad|k x|< 3 \]$$ where $$\(k\)$$ is a non-zero constant, may be written in the form $$\[ A+B x+C x^{2}+D x^{3}+\ldots \]$$ where $$\(A, B, C\)$$ and $$\(D\)$$ are constants. (a) Find the value of $$\(A\)$$ (1) Given that $$\(C=3 B\)$$ (b) show that $$\[ k^{2}+6 k=0 \]$$ (3) (c) Hence (i) find the value of $$\(k\)$$ (ii) find the value of $$\(D\)$$ (3)

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