SOLUTION: If 3+2i is a solution for x^2+mx+n=0, where m and n are real numbers, what is the value of m?

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Question 120366: If 3+2i is a solution for x^2+mx+n=0, where m and n are real numbers, what is the value of m?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If 3%2B2i is a solution, this means x=3%2B2i



x=3%2B2i Start with the given equation



x-3=2i Subtract 3 from both sides


%28x-3%29%2F2=i Divide both sides by 2 to isolate "i"


%28x-3%29%2F2=sqrt%28-1%29 Replace i with sqrt%28-1%29. Remember i=sqrt%28-1%29


%28%28x-3%29%2F2%29%5E2=-1 Square both sides



%28x-3%29%5E2%2F2%5E2=-1 Distribute the exponent



%28x-3%29%5E2%2F4=-1 Square 2 to get 4



%281%2F4%29%28x-3%29%5E2=-1 Rearrange the terms


%281%2F4%29%28x-3%29%5E2%2B1=0 Add 1 to both sides



%281%2F4%29%28x%5E2-6x%2B9%29%2B1=0 Foil


%281%2F4%29x%5E2-%283%2F2%29x%2B9%2F4%2B1=0 Distribute


%281%2F4%29x%5E2-%283%2F2%29x%2B13%2F4=0 Combine like terms



4%28%281%2F4%29x%5E2-%283%2F2%29x%2B13%2F4%29=0 Multiply both sides by the LCD 4 to eliminate any fractions


x%5E2-6x%2B13=0 Distribute. Notice how the fractions have been eliminated.



So the quadratic that has the solution 3%2B2i is y=x%5E2-6x%2B13


Since m is the coefficient for the x term in x%5E2%2Bmx%2Bn=0, this means mx=-6x and that m=-6


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Answer:

So the value of m is m=-6




Check:

You can check your answer by using the quadratic formula