The equation [tex]x^2-8x+41=0[/tex] is quadratic equation that requires finding discriminant
[tex]D=b^2-4ac=(-8)^2-4\cdot 41=64-164=-100.[/tex]
Since discriminant is negative, this equation has two complex roots. Note that [tex]-1=i^2,[/tex] where [tex]i[/tex] is imaginary unit. Then [tex]D=-100=100\cdot (-1)=100\cdot i^2,\\ \\\sqrt{D}=10i.[/tex]
Now the complex roots are
[tex]x_1=\dfrac{8+10i}{2}=4+5i,\\ \\x_2=\dfrac{8-10i}{2}=4-5i.[/tex]
Answer: correct choice is D.
