SOLUTION: If one root of a quadratic equation is 3-2i, find the other root and write the equation.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: If one root of a quadratic equation is 3-2i, find the other root and write the equation.      Log On


   

Question 552366: If one root of a quadratic equation is 3-2i, find the other root and write the equation.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If one root of a quadratic equation with real coefficients is 3-2i, the other root is 3+2i.
One equation with such roots would be
%28x-%283-2i%29%29%28x-%283%2B2i%29%29=0 --> %28x-3%2B2i%29%28x-3-2i%29=0 --> %28%28x-3%29%2B2i%29%28%28x-3%29%2B2i%29=0 --> %28x-3%29%5E2-%282i%29%5E2=0 --> x%5E2-6x%2B9-2%5E2%2Ai%5E2=0 --> x%5E2-6x%2B9-4%28-1%29=0 --> x%5E2-6x%2B9%2B4=0 --> x%5E2-6x%2B13=0
If I am not told that the coefficients are real numbers, I cannot find the other root; it could be any complex number.