SOLUTION: Show,without solving an equation that the roots of 2xsquared +(2k-1)x=K are Rational for all rational values of K

Question 1112295: Show,without solving an equation that the roots of 2xsquared +(2k-1)x=K are Rational for all rational values of K
Answer by ikleyn(52873) (Show Source): You can put this solution on YOUR website!
.

The given equation 

2x^2 +(2k-1)x = k  



is equivalent to

2x^2 +(2k-1)x - k = 0



which, in turn, is factored as


(2x-1)*(x+k) = 0


and, OBVIOUSLY, has the roots  x=   and  x= k,  that are rational numbers.

Solved and Proved.

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