document.write( "Question 844795: Find a polynomial with the following zeros. 4, 3+2i \n" ); document.write( "
Algebra.Com's Answer #508918 by josgarithmetic(39617)\"\" \"About 
You can put this solution on YOUR website!
Complex roots with imaginary components occur in conjugate pairs.\r
\n" ); document.write( "\n" ); document.write( "The root, 3-2i is also a root.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Polynomial with the three roots given is \"%28x-4%29%28x-%283-2i%29%29%28x-%283%2B2i%29%29\", and you just need to simplify to put into general form.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The multiplication and simplification:
\n" ); document.write( "You can more or less use distributive property on each of the complex factors with their imaginary components.
\n" ); document.write( "\"%28x-4%29%28x-3%2B2i%29%28x-3-2i%29\"
\n" ); document.write( "And apply an association on each of those complex factors.
\n" ); document.write( "\"%28x-4%29%28%28x-3%29%2B2i%29%28%28x-3%29-2i%29\"
\n" ); document.write( "Which neighboring factors are multiplied first does not matter. Take advantage of the difference of square result for the two complex factors with the imaginary components:
\n" ); document.write( "\"%28x-4%29%28%28x-3%29%5E2-%282i%29%5E2%29\"
\n" ); document.write( "\"%28x-4%29%28x%5E2-6x%2B9-4%28-1%29%29\"
\n" ); document.write( "\"%28x-4%29%28x%5E2-6x%2B9%2B4%29\"
\n" ); document.write( "\"highlight%28%28x-4%29%28x%5E2-6x%2B13%29%29\"-----You can take this one step further and multiply the binomial by the quadratic and put fully into general form.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%5E2%28x-4%29-6x%28x-4%29%2B13%28x-4%29\"
\n" ); document.write( "\"x%5E3-4x%5E2-6x%5E2%2B24x%2B13x-52\"
\n" ); document.write( "\"highlight%28highlight%28x%5E3-10x%5E2%2B37x-52%29%29\" \n" ); document.write( "
\n" );