It will have a double root if its discriminant b2-4ac = 0





    <-- answer

Checking:




10x-17=0;  10x-17=0
   10x=17;    10x=17
     x=;     x=

So both roots are the same, so it has a double root if 

So  is correct.

Edwin

You could also do it this way:





That would have a double root if it would factor this way,
as the sum of the square roots of the first and last terms,
with the same sign between them as the middle term has:





Then the middle term's coefficient would equal -17







 

Edwin