document.write( "Question 421955: It is given that -2 is one of the roots of the quadratic equation
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Algebra.Com's Answer #294576 by Edwin McCravy(20055)\"\" \"About 
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It is given that -2 is one of the roots of the quadratic equation
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document.write( "We get the left side into the form of a \"monic trinomial\"\r\n" );
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document.write( "x² + Bx + C = 0\r\n" );
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document.write( "and use the theorem that B is the opposite of the sum of \r\n" );
document.write( "the roots and C is the product of the roots.\r\n" );
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document.write( "h - 8x - 2x² = 0\r\n" );
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document.write( "We rearrange the left side in descending order:\r\n" );
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document.write( "-2x² - 8x + h = 0\r\n" );
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document.write( "Then we divide every term by -2\r\n" );
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document.write( "-2x²    8x     h     0\r\n" );
document.write( "———— - ———— + ——— = ———\r\n" );
document.write( " -2     -2    -2    -2\r\n" );
document.write( "               h \r\n" );
document.write( "    x² + 4x - ——— = 0\r\n" );
document.write( "               2\r\n" );
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document.write( "We first determine the other zero by using the fact that\r\n" );
document.write( "the coefficient of x, which is +4 is the sum of the roots with\r\n" );
document.write( "the opposite sign.  If the roots are r1 and r2,\r\n" );
document.write( "then  \r\n" );
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document.write( "r1 + r2 = -4  (which is +4 with the opposite sign).\r\n" );
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document.write( "We are told that r1 = -2, so we substitute that and get:\r\n" );
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document.write( "-2 + r2 = -4\r\n" );
document.write( "     r2 = -2\r\n" );
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document.write( "So both roots are the same.  Now the last term of the \"monic trinomial\"\r\n" );
document.write( "is the product of the roots, therefore\r\n" );
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document.write( "               h \r\n" );
document.write( "            - ——— = (-2)(-2)\r\n" );
document.write( "               2\r\n" );
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document.write( "               h \r\n" );
document.write( "            - ——— = 4\r\n" );
document.write( "               2\r\n" );
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document.write( "               -h = 8\r\n" );
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document.write( "                h = -8.\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "  h - 8x - 2x² = 0\r\n" );
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document.write( " -8 - 8x - 2x² = 0\r\n" );
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document.write( " -2x² - 8x - 8 = 0\r\n" );
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document.write( "   x² + 4x + 4 = 0\r\n" );
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document.write( "(x + 2)(x + 2) = 0\r\n" );
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document.write( "x + 2 =  0;  x + 2 =  0\r\n" );
document.write( "    x = -2;      x = -2 \r\n" );
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document.write( "So it checks. h = -8\r\n" );
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document.write( "Edwin
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