Question 705199
Choosing #1 and abbreviating the solution process,


General solution to quadratic equation gives, after appropriate simplification steps, {{{x=(k+sqrt(k))/k}}} or {{{x=(k-sqrt(k))/k}}}.  Now since one of the roots is 1/2, we should equate 1/2 to this expression for x  (both of them just to be thorough) and try solving for k.  


{{{1/2=(k+sqrt(k))/k}}},  and {{{1/2=(k-sqrt(k))/k}}}.
Either way ultimately gives k^2-4k=0,
{{{k(k-4)=0}}},
and since k=0 does not have any use here, we choose k=4.  


Our original quadratic equation could be amended for k=4 as,
{{{4x^2-2*4x+4-1=0}}}
{{{4x^2-8x+3=0}}}
.
...and if all was done well, one of the roots should be found to be 1/2
(but I did not yet actually check this).