document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #131577 by EMStelley(208) $\"\"$ $\"About$

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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.
\n" ); document.write( " $\"%28x-%283%2B2i%29%29%28x-%283-2i%29%29\"$
\n" ); document.write( " $\"x%5E2-x%283-2i%29-x%283%2B2i%29%2B%283%2B2i%29%283-2i%29\"$
\n" ); document.write( " $\"x%5E2-3x%2B2ix-3x-2ix%2B9-6i%2B6i-4i%5E2\"$
\n" ); document.write( " $\"x%5E2-6x%2B9-4%28-1%29\"$
\n" ); document.write( " $\"x%5E2-6x%2B13\"$
\n" ); document.write( "Thus, m=-6. \n" ); document.write( "

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