document.write( "Question 1054628: Find the polynomial function with the given zeros: 3, 3i, 3+3i. Please show all work, thank you! \n" ); document.write( "

Algebra.Com's Answer #669808 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "First we find a polynomial equation with solutions\r\n" );
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document.write( "3, 3i, 3+3i\r\n" );
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document.write( "Since 3+3i is a zero, so is its conjugate 3-3i\r\n" );
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document.write( "Since 3i is an imaginary zero, so is its conjugate. To find the \r\n" );
document.write( "conjugate of 3i, write it as 0+3i and so its conjugate is 0-3i\r\n" );
document.write( "which is just -3i.\r\n" );
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document.write( "So all the zeros are 3, 3i, -3i, 3+3i. 3-3i\r\n" );
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document.write( "Set x = to each of those:\r\n" );
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document.write( "   x=3;    x=3i;      x=-3i;    x=3+3i;      x=3-3i\r\n" );
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document.write( "Get 0 on the right side of each of those:\r\n" );
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document.write( " x-3=0;  x-3i=0;     x+3i=0;  x-3+3i=0; x-3+3i=0\r\n" );
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document.write( "Multiply all the left sides together, putting each\r\n" );
document.write( "in parentheses, ant them equl to all the right sides\r\n" );
document.write( "multiplied together.  Since the right sides are all 0, \r\n" );
document.write( "multiplying them all together gives 0. So we have:\r\n" );
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document.write( "  (x-3)(x-3i)(x+3i)(x-3+3i)(x-3+3i) = 0\r\n" );
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document.write( "That's a lot of multiplying, but when you have collected\r\n" );
document.write( "all the terms, and taken care of all the powers of i, you \r\n" );
document.write( "will have:\r\n" );
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document.write( "  \r\n" );
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document.write( "So the polynomial function that has those given zeros is\r\n" );
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document.write( "  .\r\n" );
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document.write( "Edwin

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