document.write( "Question 265412: The coefficients of a quadratic equation are positive integers and the difference between the two roots of the equation is 2. If one of the roots is -3/4, find the equation. \n" ); document.write( "
Algebra.Com's Answer #195149 by Edwin McCravy(20059)\"\" \"About 
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The coefficients of a quadratic equation are positive integers and the difference between the two roots of the equation is 2. If one of the roots is -3/4, find the equation.
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document.write( "There are two possibilities to consider, depending on which way \r\n" );
document.write( "subtracting them gives 2:\r\n" );
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document.write( "Case 1.  The roots are \"3%2F4\" and \"3%2F4%2B2\", or \"11%2F4\"\r\n" );
document.write( "Case 2.  The roots are \"3%2F4\" and \"3%2F4-2\", or \"-5%2F4\"\r\n" );
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document.write( "In case 1, the difference between the roots is \"11%2F4-3%2F4=8%2F4=2\"\r\n" );
document.write( "In case 2, the difference between the roots is \"3%2F4-%28-5%2F4%29=3%2F4%2B5%2F4=8%2F4=2\"\r\n" );
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document.write( "In case 1, the solutions would be\r\n" );
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document.write( "\"x=11%2F4\" and \"x=3%2F4\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"4x=11\" and \"4x=3\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"4x-11=0\" and \"4x-3=0\"\r\n" );
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document.write( "which would have come from using the zero-factor \r\n" );
document.write( "property of the factored equation:\r\n" );
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document.write( "\"%284x-11%29%284x-3%29=0\"\r\n" );
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document.write( "which would have come from the quadratic equation:\r\n" );
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document.write( "\"16x%5E2-12x-44x%2B33=0\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"16x%5E2-56x%2B33=0\" \r\n" );
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document.write( "But the problem said that the coefficients are positive \r\n" );
document.write( "integers.  But -56 is not positive.  So we have to discard that answer.\r\n" );
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document.write( "In case 2, the solutions would be\r\n" );
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document.write( "\"x=3%2F4\" and \"x=-5%2F4\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"4x=3\" and \"4x=-5\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"4x-3=0\" and \"4x%2B5=0\"\r\n" );
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document.write( "which would have come from using the zero-factor \r\n" );
document.write( "property of the factored equation:\r\n" );
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document.write( "\"%284x-3%29%284x%2B5%29=0\"\r\n" );
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document.write( "which would have come from the quadratic equation:\r\n" );
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document.write( "\"16x%5E2%2B20x-12x-15=0\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"16x%5E2%2B8x-15=0\" \r\n" );
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document.write( "The coefficients of \"x%5E2\" and \"x\" are both\r\n" );
document.write( "positive. So that is the only quadratic equation\r\n" );
document.write( "with the coefficients of \"x%5E2\" and \"x\" both\r\n" );
document.write( "positive integers. \r\n" );
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document.write( "Edwein
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