Respuesta :
Answer:
Option 4 - The solution of x is [tex]x=4\pm5i[/tex].
Step-by-step explanation:
Given : Equation [tex]x^2-8x+41=0[/tex]
To find : Solve for x in the equation ?
Solution :
Solving a quadratic equation [tex]ax^2+bx+c=0[/tex] solution is given by, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=1, b=-8 and c=41
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(41)}}{2(1)}[/tex]
[tex]x=\frac{8\pm\sqrt{-100}}{2}[/tex]
[tex]x=\frac{8\pm10i}{2}[/tex]
[tex]x=4\pm5i[/tex]
Therefore, the solution of x is [tex]x=4\pm5i[/tex].
