document.write( "Question 722945: Given the root 5+2i find all roots of the equation x^3-7x^2-x+87=0\r
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Algebra.Com's Answer #442962 by Edwin McCravy(20056) $\"\"$ $\"About$

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5+2i find all roots of the equation x^3-7x^2-x+87=0
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document.write( "You can use synthetic division\r\n" );
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document.write( "5+2i |1   -7     -1      87\r\n" );
document.write( "     |     5+2i  -14+6i -87\r\n" );
document.write( "      1   -2+2i  -15+6i   0\r\n" );
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document.write( "So we have factored the left side of the equation as:\r\n" );
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document.write( "[x-(5+2i)][x²+(-2+2i)x+(-15+6i)] = 0\r\n" );
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document.write( "Since 5+2i is a root, so is its conjugate 5-2i.  So\r\n" );
document.write( "we use synthetic division again on\r\n" );
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document.write( "              x²+(-2+2i)x+(-15+6i) = 0\r\n" );
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document.write( "5-2i |1   -2+2i   -15+6i\r\n" );
document.write( "     |     5-2i    15-6i\r\n" );
document.write( "      1    3         0 \r\n" );
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document.write( "So the complete factorization is\r\n" );
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document.write( "[x-(5+2i)][x+(5+2i)](x+3) = 0\r\n" );
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document.write( "Set each equal to 0 and solve \r\n" );
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document.write( "The three roots are 5+2i, 5-2i, and -3 \r\n" );
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document.write( "Edwin

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