document.write( "Question 1128592: Form a quadratic equations whose roots are 1+ sqrt2 and 1 - sqrt 2. \n" ); document.write( "
Algebra.Com's Answer #745098 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Form a quadratic \"highlight%28cross%28equations%29%29\" equation whose roots are 1+ sqrt2 and 1 - sqrt 2.
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document.write( "Use the Vieta's theorem.\r\n" );
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document.write( "The product of the roots is the constant term of the polynomial:\r\n" );
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document.write( "    \"%281%2Bsqrt%282%29%29%2A%281-sqrt%282%29%29\" = \"1%5E2+-+%28sqrt%282%29%29%5E2\" = 1 - 2 = -1.\r\n" );
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document.write( "The sum of the root is equal to \"%281%2Bsqrt%282%29%29%2A%281-sqrt%282%29%29\" = 2,\r\n" );
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document.write( "and it is the coefficient at x taken with the opposite sign.\r\n" );
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document.write( "Hence, the coefficient at x is equal to -2.\r\n" );
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document.write( "Then the equation is  \"x%5E2+-2x+-1\" = 0.\r\n" );
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