document.write( "Question 682329: Find a polynomial function of degree 3 with zeros 1/2, 1-i; where P(4) = 140 \n" ); document.write( "
Algebra.Com's Answer #423127 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Find a polynomial function of degree 3 with zeros 1/2, 1-i; where P(4) = 140
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document.write( "Since the polynomial is to have real coefficients, since 1-i is a zero,\r\n" );
document.write( "its conjugate 1+i is also a zero\r\n" );
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document.write( "So the polynomial is\r\n" );
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document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28x-1%2F2%29%28x-%281-i%29%29%28x-%281%2Bi%29%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28x-1%2F2%29%28x-1%2Bi%29%28x-1-i%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28x-1%2F2%29%28%28x-1%29%2Bi%29%28%28x-1%29-i%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28x-1%2F2%29%28%28x-1%29%5E2-i%5E2%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28x-1%2F2%29%28%28x-1%29%5E2-%28-1%29%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28x-1%2F2%29%28%28x-1%29%5E2%2B1%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%282x%2F2-1%2F2%29%28%28x%5E2-2x%2B1%29%2B1%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28%282x-1%29%2F2%29%28x%5E2-2x%2B1%2B1%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%28%282x-1%29%2F2%29%28x%5E2-2x%2B2%29\"\r\n" );
document.write( "\"2%2A%22P%28x%29%22\"\"%22%22=%22%22\"\"A%282x-1%29%28x%5E2-2x%2B2%29\"\r\n" );
document.write( "\"2%2A%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%282x%5E3-4x%5E2%2B4x-x%5E2%2B2x-2%29\"\r\n" );
document.write( "\"2%2A%22P%28x%29%22\"\"%22%22=%22%22\"\"A%2A%282x%5E3-5x%5E2%2B6x-2%29\"\r\n" );
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document.write( "Now we substitute \"%22P%284%29%22\"\"%22%22=%22%22\"\"140\", \r\n" );
document.write( "which implies that we also substitute\"x\"\"%22%22=%22%22\"\"4\".\r\n" );
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document.write( "\"2%2A%22P%284%29%22\"\"%22%22=%22%22\"\"A%282x%2A4%5E3-5%2A4%5E2%2B6%2A4-2%29\"\r\n" );
document.write( "\"2%2A140\"\"%22%22=%22%22\"\"A%2A%282%2A64-5%2A16%2B6%2A4-2%29\"\r\n" );
document.write( "\"280\"\"%22%22=%22%22\"\"A%2A%28128-80%2B24-2%29\"\r\n" );
document.write( "\"280\"\"%22%22=%22%22\"\"A%2A%2870%29\"\r\n" );
document.write( "\"280%2F70\"\"%22%22=%22%22\"\"A\"\r\n" );
document.write( "\"4\"\"%22%22=%22%22\"\"A\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"2%2A%22P%28x%29%22\"\"%22%22=%22%22\"\"4%2A%282x%5E3-5x%5E2%2B6x-2%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"2%2A%282x%5E3-5x%5E2%2B6x-2%29\"\r\n" );
document.write( "\"%22P%28x%29%22\"\"%22%22=%22%22\"\"4x%5E3-10x%5E2%2B12x-4\"\r\n" );
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document.write( "Edwin
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