C. because a > 0, the opening is upward and the symmetry axis is unknown, there are three cases: 1. If the function image does not intersect with the x axis, the equation has no real root. 2. The function image has an intersection with the X axis. At this time, the equation has a solution, and A and B are on both sides of the symmetry axis. 3. The function has two intersections with the x axis, and the equation has two solutions, X 1 and X2. If a and b are both on the left or right of X 1, the equation of interval (a, b) has no solution. If a is to the left of X 1 and b is to the right of X2, that is, X 1X2 belongs to the interval (a, b). To sum up, so choose C, there may be two schemes.