To find:
The number of times graph intersect or touch the x-axis.
Solution:
It is known that the graph touches or intersect x-axis where y = 0. So, the graph touches or intersects when -3x²+x+4 = 0.
The above equation is a quadratic equation. The quadratic equation has two distinct real solutions.
Thus, the graph intersects or touches the x-axis at exactly two points.
So, the third option is correct.
