document.write( "Question 279010: Find all other zeros of \"P%28x%29=+x%5E3+-+11x+%2B+20\" , given that 2-i is a zero.\r
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Algebra.Com's Answer #202944 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First write \"P%28x%29=x%5E3+-+11x+%2B+20\" as \r\n" );
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document.write( "\"P%28x%29=x%5E3+%2B0x%5E2-+11x+%2B+20\"\r\n" );
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document.write( "Then you can use synthetic division with the zero 2-i\r\n" );
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document.write( "2-i | 1    0     -11     20\r\n" );
document.write( "    !      2-i\r\n" );
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document.write( "      1    2-i\r\n" );
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document.write( "Now we have to stop and multiply 2-i by 2-i\r\n" );
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document.write( "\"%282-i%29%282-i%29=4-2i-2i%2Bi%5E2=4-4i%2Bi%5E2=4-4i%2B%28-1%29=3-4i\"\r\n" );
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document.write( "Continuing with the synthetic division:\r\n" );
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document.write( "2-i | 1    0     -11     20\r\n" );
document.write( "    !      2-i     3-4i\r\n" );
document.write( "     ----------------------\r\n" );
document.write( "      1    2-i    -8-4i\r\n" );
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document.write( "Now we have to stop again and multiply -8-4i by 2-i\r\n" );
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document.write( "\"%28-8-4i%29%282-i%29=-16%2B8i-8i%2B4i%5E2=-16%2B4i%5E2=-16%2B4%28-1%29=-16-4=-20\"\r\n" );
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document.write( "Continuing with the synthetic division:\r\n" );
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document.write( "2-i | 1    0     -11     20\r\n" );
document.write( "    |      2-i     3-4i -20\r\n" );
document.write( "     ----------------------\r\n" );
document.write( "      1    2-i    -8-4i   0\r\n" );
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document.write( "So we have factored \r\n" );
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document.write( "\"P%28x%29=x%5E3+-+11x+%2B+20\"\r\n" );
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document.write( "as\r\n" );
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document.write( "P(x) = [x - (2-i)][x² + (2-i)x + (-8-4i)]\r\n" );
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document.write( "Now since 2-i is a zero, so is its conjugate is 2+i\r\n" );
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document.write( "So we use synthetic division with the second factor\r\n" );
document.write( "and zero 2+i\r\n" );
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document.write( "2+i | 1    2-i   -8-4i\r\n" );
document.write( "    |      2+i    8+4i     \r\n" );
document.write( "     -----------------\r\n" );
document.write( "      1    4       0\r\n" );
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document.write( "Now we have completed the factoring of \r\n" );
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document.write( "\"P%28x%29=x%5E3+-+11x+%2B+20\"\r\n" );
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document.write( "as\r\n" );
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document.write( "P(x) = [x - (2-i)][x - (2+i)](x + 4)\r\n" );
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document.write( "So now we see that the third zero is -4.\r\n" );
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document.write( "So the three zeros of P(x) are 2-i, 2+i, and -4.\r\n" );
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document.write( "Edwin
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