document.write( "Question 747996: Find the polynomial equation with integral coefficients that has the given roots: -2, i, -i. \n" ); document.write( "

Algebra.Com's Answer #455272 by Edwin McCravy(20056) $\"\"$ $\"About$

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Find the polynomial equation with integral coefficients that has the given roots: -2, i, -i
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document.write( "It's a matter of solving it backwards. You start\r\n" );
document.write( "with three equations with x equaling to them:\r\n" );
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document.write( "        x=-2,  x=i.   x=-i\r\n" );
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document.write( "Get 0 on the right of each of these because that\r\n" );
document.write( "would have been the next to last step of solving\r\n" );
document.write( "the equation: \r\n" );
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document.write( "       x+2=0, x-i=0, x+i=0\r\n" );
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document.write( "Before that was the zero factor principle, so to \r\n" );
document.write( "reverse that we multiply all three equation together\r\n" );
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document.write( "       (x+2)(x-i)(x+i) = 0\r\n" );
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document.write( "           (x+2)(x²-i²) = 0\r\n" );
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document.write( "Then use the fact that i² = -1\r\n" );
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document.write( "            (x+2)(x²-(-1)) = 0\r\n" );
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document.write( "               (x+2)(x²+1) = 0\r\n" );
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document.write( "                x³+x+2x²+2 = 0\r\n" );
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document.write( "Putting the terms in descending order:\r\n" );
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document.write( "                x³+2x²+x+2 = 0\r\n" );
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document.write( "Edwin

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