OG详解-OG1 数学1 Q12

Choice C is correct. If a value of x  satisfies f(x)=0, the graph of  y = f(x) will contain a point ( x,0 ) and thus touch the x-axis. Since there are 3 points at which this graph touches the x-axis, there are 3 values of x for which f(x)=0.
Choice A is incorrect and may result from conceptual or calculation errors. 
Choice B is incorrect and may result from conceptual or calculation errors. 
Choice D is incorrect and may result from conceptual or calculation errors.