document.write( "Question 187719: Find the quadratic equation with roots (4+i) and (4-i) \n" ); document.write( "
Algebra.Com's Answer #140758 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"x=4%2Bi\" or \"x=4-i\" Start with the given roots.\r
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\n" ); document.write( "\n" ); document.write( "\"x-4=i\" or \"x-4=-i\" Get the real numbers to the left side.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-4%29%5E2=%28i%29%5E2\" or \"%28x-4%29%5E2=%28-i%29%5E2\" Square both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-4%29%5E2=-1\" or \"%28x-4%29%5E2=-1\" Square \"i\" to get -1. Square \"-i\" to get -1. \r
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\n" ); document.write( "\n" ); document.write( "Since these equations are identical, this means that we can use one equation\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-4%29%5E2=-1\" \r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-8x%2B16=-1\" FOIL the left side\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-8x%2B16%2B1=0\" Add 1 to both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-8x%2B17=0\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So the quadratic equation that has the roots 4+i and 4-i is \"y=x%5E2-8x%2B17\"
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