SOLUTION: Hi- I have a hard time understanding what to do for this problem. Here it is: Find a quadratic equation that has (3+2i) as a root. I know the answer is x²-6x+13=0, but how

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi- I have a hard time understanding what to do for this problem. Here it is: Find a quadratic equation that has (3+2i) as a root. I know the answer is x²-6x+13=0, but how       Log On


   

Question 163809: Hi-
I have a hard time understanding what to do for this problem. Here it is:
Find a quadratic equation that has (3+2i) as a root.
I know the answer is x²-6x+13=0, but how is found, what do you do, etc?
Answer by NotGoodAtAlgebra(1) About Me  (Show Source):
You can put this solution on YOUR website!
YES! I FIGURED IT OUT! YES!
This is the same guy who asked it. In case anyone was interested:
root= (3+2i)
ax²+bx+c is the equation set up.
root1 + root2 = -b (-6x in this quadratic equation)
root1 * root2 = c (13 in this equation)
then there is x² at the beginning.
root1 + root2 = 6 in this equation because the + and the - imaginary numbers in the equation equal 0, so 3+3 will equal 6. Then you will have -b, so it will be -6x.
(3+2i)*(3-2i)= 9-6i + 6i-4i² = 9 + 0 + 4 = 13
so:
x²-6x+13 = 0
Then, plugging in the root for x on a calculator, you will find:
(3+2i)² - 6(3+2i) + 13 = 0
I'm so happy I solved this. I have to get sleep now though. I go to school in 3 hours lol.