If the equation

(a) 1 or 4

It is given that the roots of the equation $\left(x^{2}+2(k+2) x+9 k=0\right)$ are equal.

$\therefore\left(b^{2}-4 a c\right)=0$

$\Rightarrow\{2(k+2)\}^{2}-4 \times 1 \times 9 k=0$

$\Rightarrow 4\left(k^{2}+4 k+4\right)-36 k=0$

$\Rightarrow 4 k^{2}+16 k+16-36 k=0$

$\Rightarrow 4 k^{2}-20 k+16=0$

$\Rightarrow k^{2}-5 k+4=0$

$\Rightarrow k^{2}-4 k-k+4=0$

$\Rightarrow k(k-4)-(k-4)=0$

$\Rightarrow(k-4)(k-1)=0$

$\Rightarrow k=4$ or $k=1$