The necessary and sufficient condition is that the discriminant of the quadratic equation is zero

    d = b^2 - 4ac = 0,

or

    34^2 - 4k^2 = 0,

which gives

    k^2 = 

    k   = +/-  = +/-  = +/- 17.


ANSWER.  There are two values of k satisfying the imposed condition:  k = 17  and  k = -17.