document.write( "Question 636348: what is the lowest-degree polynomial with integer coefficients and the roots 6, i, and -i?
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\n" ); document.write( "\n" ); document.write( "I think its d? \n" ); document.write( "

Algebra.Com's Answer #400928 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
what is the lowest-degree polynomial with integer coefficients and the roots 6, i, and -i?
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document.write( "It doesn't work to guess.\r\n" );
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document.write( "Set x = to each root:\r\n" );
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document.write( "     x=6,   x=i,   x=-i\r\n" );
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document.write( "Get 0 on the right side of each:\r\n" );
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document.write( "   x-6=0  x-i=0, x+i=0\r\n" );
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document.write( "Indicate the multiplication of all\r\n" );
document.write( "three left sides and set equal to 0:\r\n" );
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document.write( "    (x-6)(x-i)(x+i) = 0\r\n" );
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document.write( "Multiply two of them (the easiest is the\r\n" );
document.write( "second and third, since they are conjugates:\r\n" );
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document.write( "       (x-6)(x²-i²) = 0\r\n" );
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document.write( "Use the fact that i²=-1 to replace i²\r\n" );
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document.write( "     (x-6)[x²-(-1)] = 0\r\n" );
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document.write( "        (x-6)(x²+1) = 0\r\n" );
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document.write( "Multiply the left side out:\r\n" );
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document.write( "         x³+x-6x²-6 = 0\r\n" );
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document.write( "Arrange in descending powers of x:\r\n" );
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document.write( "         x³-6x²+x-6 = 0  \r\n" );
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document.write( "So you see that the answer is c., not d.\r\n" );
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document.write( "Edwin

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