SOLUTION: If one root of a quadratic equation is 1/2-2i, what is the equation?

Algebra ->  Trigonometry-basics -> SOLUTION: If one root of a quadratic equation is 1/2-2i, what is the equation?       Log On


   

Question 443124: If one root of a quadratic equation is 1/2-2i, what is the equation?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If one root of a quadratic equation is 1/2-2i, what is the equation?
x = 1%2F2 - 2i
We can write it
x = .5 - 2i
x - .5 = -2i
Square both sides, FOIL the left side
x^2 - 1x + .25 = 4i^2
we know i^2 = -1, therefore
x^2 - x + .25 = 4(-1)
x^2 - x + .25 = -4
x^2 - x + .25 + 4 = 0
x^2 - x + 4.25 = 0; the equation