document.write( "Question 1191999: Form a fifth-degree polynomial function with real coefficients such that 5i, 1-3i, and -3 are zeros and f(0)=1500 \n" ); document.write( "

Algebra.Com's Answer #823880 by Edwin McCravy(20062) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Instead of doing your problem for you, I'm going to do \r\n" );
document.write( "one exactly like it instead, step by step.  Here's the one I'm \r\n" );
document.write( "going to do. Use it as a model for yours.

\n" ); document.write( "Form a fifth-degree polynomial function with real coefficients
\n" ); document.write( "such that 6i, 1-4i, and -4 are zeros and f(0)=7344
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document.write( "If a polynomial with real coefficients has a complex imaginary zero,\r\n" );
document.write( "its conjugate is also a zero.\r\n" );
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document.write( "Since 6i is a zero, so is -6i.\r\n" );
document.write( "Since 1-4i is a zero, so is 1+4i.\r\n" );
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document.write( "x-6i, x-(-6i), x-(1-4i), x-(1+4i), x-(-4) are all factors. Simplifying them:\r\n" );
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document.write( "x-6i, x+6i, x-1+4i, x-1-4i, x+4\r\n" );
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document.write( "So f(x) must be some constant \"a\" times the product of those factors:\r\n" );
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document.write( "Multiply that out:\r\n" );
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document.write( "It makes it a little easier to group the real parts of conjugates:\r\n" );
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document.write( "Since i² = -1\r\n" );
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document.write( "Since f(0)=7344,\r\n" );
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document.write( "So\r\n" );
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document.write( "Edwin

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