OG详解-OG7 数学1 Q27

The correct answer is either 14, -5, or -4. The x-intercepts of a graph in the xy-plane are the points at which the graph intersects the x-axis, or when the value of y is 0. Substituting 0 for y in the given equation yields 0 = 3(x-14)(x+5)(x+4). Dividing both sides of this equation by 3 yields 0 = (x-14)(x+5)(x+4). Applying the zero product property to this equation yields three equations: x-14 = 0, x+5 = 0, and x+4 = 0. Adding 14 to both sides of the equation x- 14 = 0 yields x = 14, subtracting 5 from both sides of the equation x+5 = 0 yields x =-5, and subtracting 4 from both sides of the equation x+4 = 0 yields x =-4. Therefore, the x-coordinates of the x-intercepts of the graph of the given equation are 14, -5, and -4. Note that 14, -5, and -4 are examples of ways to enter a correct answer.