Question

Solve x2 – 8x + 41 = 0 for x.

Answer 1

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 $D=-100=100\cdot (-1)=100\cdot i^2,\\ \\\sqrt{D}=10i.$

Now the complex roots are

$x_1=\dfrac{8+10i}{2}=4+5i,\\ \\x_2=\dfrac{8-10i}{2}=4-5i.$

Answer: correct choice is D.

Answer 2

Answer:

x+4+-5i

Step-by-step explanation: