document.write( "Question 825531: The roots of the quadratic equation x^2-7x+c differ by 1. Find c \n" ); document.write( "

Algebra.Com's Answer #497365 by Edwin McCravy(20056) $\"\"$ $\"About$

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The roots of the quadratic equation x²-7x+c = 0
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document.write( "let r = one root and r-1 be the other root.\r\n" );
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document.write( "Substitute r for x:\r\n" );
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document.write( "Eq. 1:      r²-7r+c = 0\r\n" );
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document.write( "Substitute (r-1) for x\r\n" );
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document.write( "Eq. 2:     (r-1)²-7(r-1)+c = 0\r\n" );
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document.write( "Simplify Eq. 2:\r\n" );
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document.write( "         (r-1)(r-1)-7r+7+c = 0\r\n" );
document.write( "            r²-2r+1-7r+7+c = 0\r\n" );
document.write( "                 r²-9r+8+c = 0\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "Get the 8 off the right side of the second equation by\r\n" );
document.write( "adding -8 to both sides\r\n" );
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document.write( "Multiply the second equation by -1 and add the two equations term by term:\r\n" );
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document.write( " r²-7r+c = 0\r\n" );
document.write( "-r²+9r-c = 8\r\n" );
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document.write( "    2r   = 8\r\n" );
document.write( "       r = \r\n" );
document.write( "       r = 4\r\n" );
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document.write( "Substitute that in \r\n" );
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document.write( "         r²-7r+c = 0\r\n" );
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document.write( "       \r\n" );
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document.write( "            \r\n" );
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document.write( "                     \r\n" );
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document.write( "Edwin

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