Answer:
Solving the equation [tex]x^2-8x+41=0[/tex] using quadratic formula we get [tex]x=4+5i \ or \ x=4-5i[/tex]
Step-by-step explanation:
We need to solve the equation [tex]x^2-8x+41=0[/tex] using quadratic formula.
The quadratic formula is:
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
where a=1, b=-8 and c=41
Putting values in formula and finding x
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$\\$x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(41)}}{2(1)}$\\$x=\frac{8\pm\sqrt{64-164}}{2}$\\$x=\frac{8\pm\sqrt{-100}}{2}$\\We \ know \ \sqrt{-1}=i\\x=\frac{8\pm10i}{2}\\x=\frac{8+10i}{2} \ or \ x=\frac{8-10i}{2}\\x=4+5i \ or \ x=4-5i[/tex]
So, Solving the equation [tex]x^2-8x+41=0[/tex] using quadratic formula we get [tex]x=4+5i \ or \ x=4-5i[/tex]
