OG详解-OG5 数学1 Q21

The correct answer is 336. By the zero product property, if (x+14)(t-x) = 0, then x+14 = 0, which gives x =-14, or (t-x) = 0, which gives x = t. Therefore, g(x) = 0 when x = -14 and when x = t. Since the graph of y = g(x) passes through the point (24, 0), it follows that g(24) = 0, so t = 24. Substituting 24 for t in the equation g(x) = (x+14)(t-x) yields g(x) = (x+14)(24-x). The value of g(0) can be calculated by substituting 0 for x in this equation, which yields g(0) = (0+14)(24-0), or g(0) = 336.