(i) The given equation is $9 x^{2}+3 k x+4=0$.

$\therefore D=(3 k)^{2}-4 \times 9 \times 4=9 k^{2}-144$

The given equation has real and distinct roots if $D>0 .$

$\begin{array}{l}
\therefore 9 k^{2}-144>0 \\
\Rightarrow 9\left(k^{2}-16\right)>0 \\
\Rightarrow(k-4)(k+4)>0 \\
\Rightarrow k<-4 \text { or } k>4
\end{array}$

(ii) The given equation is $5 x^{2}-k x+1=0$.

$\therefore D=(-k)^{2}-4 \times 5 \times 1=k^{2}-20$

The given equation has real and distinct roots if $D>0$.

$\begin{array}{l}
\therefore k^{2}-20>0 \\
\Rightarrow k^{2}-(2 \sqrt{5})^{2}>0 \\
\Rightarrow(k-2 \sqrt{5})(k+2 \sqrt{5})>0 \\
\Rightarrow k<-2 \sqrt{5} \text { or } k>2 \sqrt{5}
\end{array}$