document.write( "Question 1112295: Show,without solving an equation that the roots of 2xsquared +(2k-1)x=K are Rational for all rational values of K \n" ); document.write( "

Algebra.Com's Answer #727320 by ikleyn(52874) $\"\"$ $\"About$

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document.write( "The given equation \r\n" );
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document.write( "2x^2 +(2k-1)x = k  \r\n" );
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document.write( "is equivalent to\r\n" );
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document.write( "2x^2 +(2k-1)x - k = 0\r\n" );
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document.write( "which, in turn, is factored as\r\n" );
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document.write( "(2x-1)*(x+k) = 0\r\n" );
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document.write( "and, OBVIOUSLY, has the roots  x=   and  x= k,  that are rational numbers.\r\n" );
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