document.write( "Question 1181679: If -2 is a root of $\"+z%5E3+-+8z%5E2+%2B+9z+%2B+58+=+0+\"$ , then find the other two roots. \n" ); document.write( "

Algebra.Com's Answer #811579 by ikleyn(52756) $\"\"$ $\"About$

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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( "Find the roots of the last quadratic polynomial 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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