document.write( "Question 1068977: Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and zeros of 4, 1-3i, and 2+2i. \n" ); document.write( "
Algebra.Com's Answer #684206 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "zeros: 4, 1-3i, and 2+2i\r\n" );
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document.write( "Since 1-3i is a zero, so is 1+3i\r\n" );
document.write( "Since 2+2i is a zero, so is 2-2i\r\n" );
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document.write( "So we have\r\n" );
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document.write( "x=4;    x=1-3i;    x=1+3i;    x=2+2i;    x=2-2i\r\n" );
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document.write( "Get 0 on the right of each of those:\r\n" );
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document.write( "x-4=0;  x-1+3i=0;  x-1-3i=0;  x-2-2i=0   x-2+2i=0\r\n" );
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document.write( "x-4=0;  (x-1)+3i=0;  (x-1)-3i=0;  (x-2)-2i=0   (x-2)+2i=0\r\n" );
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document.write( "Put parentheses around the first two terms in the last 4\r\n" );
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document.write( "Multiply equals by equals to get the polynomial function p(x)\r\n" );
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document.write( "p(x) = (x-4)[(x-1)+3i][(x-1)-3i][(x-2)-2i][(x-2)+2i] = 0\r\n" );
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document.write( "p(x) = (x-4){[(x-1)+3i][(x-1)-3i]}{[(x-2)-2i][(x-2)+2i]} = 0\r\n" );
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document.write( "p(x) = (x-4){(x-1)2-9i2}{(x-2)2-4i2} = 0\r\n" );
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document.write( "p(x) = (x-4){(x-1)2-9(-1)}{(x-2)2-4(-1)} = 0\r\n" );
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document.write( "p(x) = (x-4){(x-1)2+9}{(x-2)2+4} = 0\r\n" );
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document.write( "p(x) = (x-4){(x-1)2(x-2)2+ 4(x-1)2+9(x-2)2+36} = 0\r\n" );
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document.write( "p(x) = (x-4){(x-1)2(x-2)2+ 13(x-1)2+36} = 0\r\n" );
document.write( "...\r\n" );
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document.write( "Keep on multiplying out and collecting like terms and \r\n" );
document.write( "you'll end up with this:\r\n" );
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document.write( "p(x) = x5-10x4+50x3-160x2+304x-320 \r\n" );
document.write( "  \r\n" );
document.write( "Edwin
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