SOLUTION: One solution to a quadratic equation is 4 - 5i. Find the equation. A) x2 - 18x - 65 B) x2 - 8x + 41 C) x2 + 41 Eliminate D) Not possible, you need 2 solutions to w

Algebra ->  Equations -> SOLUTION: One solution to a quadratic equation is 4 - 5i. Find the equation. A) x2 - 18x - 65 B) x2 - 8x + 41 C) x2 + 41 Eliminate D) Not possible, you need 2 solutions to w      Log On


   

Question 951660:
One solution to a quadratic equation is 4 - 5i. Find the equation.
A)
x2 - 18x - 65
B)
x2 - 8x + 41
C)
x2 + 41
Eliminate
D)
Not possible, you need 2 solutions to write the equation

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Equation B:
x2 - 8x + 41
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B41+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-8%29%5E2-4%2A1%2A41=-100.

The discriminant -100 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -100 is + or - sqrt%28+100%29+=+10.

The solution is x%5B12%5D+=+%28--8%2B-+i%2Asqrt%28+-100+%29%29%2F2%5C1+=++%28--8%2B-+i%2A10%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B41+%29

The solution%28-%28-8%29%2B-10i%29%2F2=4%2B5ior4-5i
The answer is equation(B).