document.write( "Question 1171426: Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies
\n" ); document.write( "the given condition.
\n" ); document.write( "−4i, 4i, 2; f(1) = 51 \n" ); document.write( "
Algebra.Com's Answer #796613 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing your problem for you, I'll do one exactly like it that uses\r\n" );
document.write( "exactly the same steps.  I'll do this one instead and you can use it as a\r\n" );
document.write( "model to go by:\r\n" );
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\n" ); document.write( "Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies
\n" ); document.write( "the given condition.−5i, 5i, 3; f(2) = 116
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document.write( "x = -5i; x = 5i; x = 3;\r\n" );
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document.write( "x + 5i = 0; x - 5i = 0; x - 3 = 0\r\n" );
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document.write( "Multiply left and right sides together\r\n" );
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document.write( "(x + 5i)(x - 5i)(x - 3) = 0\r\n" );
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document.write( "Multiply the first two parentheses using FOIL:\r\n" );
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document.write( "\"%28x%5E2-25i%5E2%29%28x-3%5E%22%22%29=0\"\r\n" );
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document.write( "Since i2 = -1 substitute that:\r\n" );
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document.write( "\"%28x%5E2-25%28-1%29%5E%22%22%29%28x-3%5E%22%22%29=0\"\r\n" );
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document.write( "\"%28x%5E2%2B25%5E%22%22%29%28x-3%5E%22%22%29=0\"\r\n" );
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document.write( "Use FOIL again:\r\n" );
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document.write( "\"x%5E3-3x%5E2%2B25x-75=0\"\r\n" );
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document.write( "So f(x) is a constant k times the left side of that:\r\n" );
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document.write( "\"%22f%28x%29%22=k%28x%5E3-3x%5E2%2B25x-75%29\"\r\n" );
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document.write( "Since f(2) = 116, we substitute x=2\r\n" );
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document.write( "\"%22f%282%29%22=k%282%5E3-3%282%29%5E2%2B25%282%29-75%29\"\r\n" );
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document.write( "\"116=k%282%5E3-3%282%29%5E2%2B25%282%29-75%29\"\r\n" );
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document.write( "\"116=k%288-3%284%29%2B50-75%5E%22%22%29\"\r\n" );
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document.write( "\"116=k%288-12%2B50-75%5E%22%22%29\"\r\n" );
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document.write( "\"116=k%28-29%29\"\r\n" );
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document.write( "\"%28116%29%2F%28-29%29=k\"\r\n" );
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document.write( "\"-4=k\"\r\n" );
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document.write( "\"%22f%28x%29%22=-4%28x%5E3-3x%5E2%2B25x-75%29\"\r\n" );
document.write( " \r\n" );
document.write( "\"%22f%28x%29%22=-4x%5E3%2B12x%5E2-100x%2B300\"\r\n" );
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document.write( "Now do yours exactly the same way.\r\n" );
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document.write( "Edwin
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