The given quadratic equation is:
[tex]x^2-6x+13=0[/tex]
The quadratic formula is given by the equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac^{}}}{2a}[/tex]
From the given quadratic equation;
[tex]a=1;b=-6\text{ and c=13}[/tex]
Thus, we have:
[tex]x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(13)}}{2(1)}[/tex]
[tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36-52}}{2} \\ x=\frac{6\pm\sqrt[]{-16}}{2} \\ In\text{ complex form, the }\sqrt[]{-16}=4i \\ \text{Thus, we have:} \\ x=\frac{6\pm4i}{2} \\ x=\frac{6}{2}\pm\frac{4i}{2} \\ x=3\pm2i \end{gathered}[/tex]
Hence, the correct option is Option A
