document.write( "Question 986624: Find a polynomial function with the integer coefficients that has the given zeros:\r
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Algebra.Com's Answer #607472 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since 2 is written twice, I assume you mean the polynomial is to have\r\n" );
document.write( "2 twice as a zero, or of multiplicity 2.\r\n" );
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document.write( "Conjugates of surds and complex numbers are also zeros:\r\n" );
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document.write( "\"x=1%2Bsqrt%283%29i\", \"x=1-sqrt%283%29i\", \"x=2\", \"x=2\", \"x=-1-sqrt%282%29\", \"x=-1%2Bsqrt%282%29\"\r\n" );
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document.write( "\"x-1-sqrt%283%29i=0\", \"x-1%2Bsqrt%283%29i=0\", \"x-2=0\", \"x-2=0\", \"x%2B1%2Bsqrt%282%29=0\", \"x%2B1-sqrt%282%29=0\"\r\n" );
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document.write( "Multiply all that out.  Takes a long time:\r\n" );
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document.write( "\"x%5E6-4x%5E5%2B3x%5E4%2B14x%5E3-48x%5E2%2B56x-16=0\"\r\n" );
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document.write( "So polynomial that has those zeros is\r\n" );
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document.write( "\"f%28x%29=x%5E6-4x%5E5%2B3x%5E4%2B14x%5E3-48x%5E2%2B56x-16\"\r\n" );
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document.write( "Edwin

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