SOLUTION: 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.

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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.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Basically what to do is this:

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.

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.



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When tried found roots -k and 1%2F2.
Not conclusive enough because no specified requirement that k be rational.
Equation would be 2x%5E2%2B%282k-1%29x-k=0.
Roots would be , after much simplification, %281-2k%2B-+%282k%2B1%29%29%2F4.