document.write( "Question 948574: Please help me answer this: Show, without solving the equation, that the roots of 2x^2+(2k-1)x=k are rational for all rational values of k. \n" ); document.write( "

Algebra.Com's Answer #579004 by josgarithmetic(39617) $\"\"$ $\"About$

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Basically what to do is this:\r
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\n" ); document.write( "\n" ); document.write( "Convert the equation into general form showing quadratic expression in general form equaling to zero. The coefficients may be expressions including k for a couple of them. General form is like ax^2+bx+c.\r
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\n" ); document.write( "\n" ); document.write( "Use the general solution of a quadratic equation to form the ROOTS of the equation. Simplify. The roots should be rational but not necessarily integers. \r
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\n" ); document.write( "When tried found roots $\"-k\"$ and $\"1%2F2\"$ .
\n" ); document.write( "Not conclusive enough because no specified requirement that k be rational.
\n" ); document.write( "Equation would be $\"2x%5E2%2B%282k-1%29x-k=0\"$ .
\n" ); document.write( "Roots would be , after much simplification, $\"%281-2k%2B-+%282k%2B1%29%29%2F4\"$ . \n" ); document.write( "

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