document.write( "Question 1181497: If -2 is a root of ((z^3) - (8(z^2)) + (9z) + 58 = 0, what are the other two roots? \n" ); document.write( "

Algebra.Com's Answer #811411 by ikleyn(52777) $\"\"$ $\"About$

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\n" ); document.write( "If -2 is a root of ((z^3) - (8(z^2)) + (9z) + 58 = 0, what are the other two roots?
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document.write( "In fact, -2 is a root of the given polynomial, and you can check it in one line, \r\n" );
document.write( "substituting the value of -2 into the polynomial\r\n" );
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document.write( "     -  +  + 58 = -8 - 32 - 18 + 58 = 0.\r\n" );
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document.write( "Therefore, the given polynomial is divisible by (z-2) without a remainer (according to the Remainder theorem)\r\n" );
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document.write( "and you can divide it using standard long division procedure \r\n" );
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document.write( "     = z^2 - 10z + 29.\r\n" );
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document.write( "Solve this quadratic equation using the Quadratic Formula\r\n" );
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document.write( "     =  =  =  = 5 +- 2i.\r\n" );
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document.write( "ANSWER.  Two other roots of the given equation are  (5+2i)  and  (5-2i).\r\n" );
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