SOLUTION: This is related to quadratic equations and complex numbers. The equation is x^2+mx+n=0 One of the roots/solutions is 3+2i. What is the value of m?

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Question 176455: This is related to quadratic equations and complex numbers. The equation is x^2+mx+n=0 One of the roots/solutions is 3+2i. What is the value of m?
Found 2 solutions by EMStelley, Mathtut:
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem you need to know a property of quadratic equations with complex roots. If a+bi is a solution of a quadratic equation, so is a-bi. So since 3+2i is a solution, 3-2i is also. Now, since 3+2i is a solution, that means that (x-(3+2i)) is a factor. Thus (x-(3-2i)) is a factor also. So if we multiply the two together, we should get our equation.
%28x-%283%2B2i%29%29%28x-%283-2i%29%29
x%5E2-x%283-2i%29-x%283%2B2i%29%2B%283%2B2i%29%283-2i%29
x%5E2-3x%2B2ix-3x-2ix%2B9-6i%2B6i-4i%5E2
x%5E2-6x%2B9-4%28-1%29
x%5E2-6x%2B13
Thus, m=-6.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
if one solution is 3+2i then the other is 3-2i
:
%28x-%283%2B2i%29%29%28x-%283-2i%29%29=0
:
%28x-3-2i%29%28x-3%2B2i%29=0
:
x%5E2-3x%2B2ix-3x%2B9-6i-2ix%2B6i-4i%5E2
:
x%5E2-6x%2B13=0
:
value of m=-6