Solution:
Given:
[tex]5\pm i\sqrt{2}[/tex]
The roots of the quadratic equation are;
[tex]\begin{gathered} x=5\pm i\sqrt{2} \\ x=5+i\sqrt{2}\text{ OR }x=5-i\sqrt{2} \\ \\ The\text{ factors from the root are:} \\ (x-5-i\sqrt{2})=0\text{ OR }(x-5+i\sqrt{2})=0 \\ \\ As\text{ a quadratic equation:} \\ (x-5-i\sqrt{2})(x-5+i\sqrt{2})=0 \end{gathered}[/tex]
Expanding the factors further;
[tex]\begin{gathered} (x-5-i\sqrt{2})(x-5+i\sqrt{2})=0 \\ x^2-5x+ix\sqrt{2}-5x+25-5i\sqrt{2}-ix\sqrt{2}+5i\sqrt{2}+2=0 \\ Collecting\text{ the like terms and simplifying further:} \\ x^2-5x-5x+ix\sqrt{2}-ix\sqrt{2}-5i\sqrt{2}+5i\sqrt{2}+25+2=0 \\ x^2-10x+27=0 \end{gathered}[/tex]
Therefore, the quadratic equation is;
[tex]x^2-10x+27=0[/tex]
