Explanation

The discriminant is D = 49+56(k²−7/8) = 56k². For integral roots D must be a perfect square; 56k² = (2k)²·14, and 14 is not a square, so no non-zero integer k works. For k = 0, D = 0 gives the double root −7/2, also not integral. Hence there is no integral root. Option (C).