$$\begin{gathered} {\mathrm{x}}^2-8\mathrm{kx}+16\left({\mathrm{k}}^2-\mathrm{k}+1\right)=0 \\ \mathrm{\Delta }=64{\mathrm{K}}^2-64\left({\mathrm{k}}^2-\mathrm{K}+1\right)=64(\mathrm{k}-1)>0\Rightarrow \mathrm{k}>1\to 1 \\ \begin{array}{l}4<-\frac{\mathrm{b}}{2\mathrm{a}}=\frac{8\mathrm{k}}{2}\Rightarrow \mathrm{k}>1\to 2\\ \begin{array}{ll}\mathrm{f}\left(4\right)\ge 0& \Rightarrow 16-32\mathrm{k}+16{\mathrm{k}}^2-16\mathrm{k}+16\ge 0\end{array}\end{array} \\ \begin{array}{l}\Rightarrow {\mathrm{k}}^2-3\mathrm{k}+2\ge 0\Rightarrow (\mathrm{k}-1)(\mathrm{k}-2)\ge 0\\ \Rightarrow \mathrm{k}\le 1\text{ or }\mathrm{K}\ge 2\to 3\end{array} \end{gathered}$$
from k satisfies least integer as 2.