Question

Solve x2 – 8x + 41 = 0 for x.

x=-4 (-+)square root of 37i
x = –4 ± 5i

x=4(-+) square root of 37i
x = 4 ± 5i

Answer 1

x+4+-5i

Explanation:

Answer 2

The equation
`x^2-8x+41=0` is quadratic equation that requires finding discriminant

`D=b^2-4ac=(-8)^2-4\cdot 41=64-164=-100.`

Since discriminant is negative, this equation has two complex roots. Note that
`-1=i^2,` where
`i` is imaginary unit. Then
`D=-100=100\cdot (-1)=100\cdot i^2,\\ \\√(D)=10i.`

Now the complex roots are

`x_1=(8+10i)/(2)=4+5i,\\ \\x_2=(8-10i)/(2)=4-5i.`

Answer: correct choice is D.