 The graph of a polynomial y equals to p of x is given below. This is the graph that we are talking about. Find the number of zeros of p of x. But before moving towards the solution of this question, let us spend some more time on this graph given here. Why? Because later on this would really help us to visualize the number of zeros that we need here. All the points on this y-axis represent the value of this polynomial p of x. And all the points on this x-axis represent all the values of the input variable, the variable from which this polynomial is made up of. And let us say that we take any random point on this graph, let us say this point. So this would be my corresponding x-coordinate, let us call this x1. The y-coordinate of this point would represent the value of the function for this particular x-value. So this would be p of x1. And this would be true for any point on the graph here. So now, if you already know what zeros are and if you were just struggling with like how to see them on the graph, you can just go ahead and try this question on your own now. For rest of us, let us try to understand what do we mean by zero of a polynomial? What do we actually mean by zero? Let's take a quick example. Let's say that we have another polynomial. Let us represent it by some f of x equals to x minus 2. So if I may ask you, for what value of x is the value of this polynomial equal to zero? So the answer would be x equals to 2. The moment we substitute 2 instead of x, the value of the polynomial would become zero. 2 minus 2 equal to zero. So this x equals to 2, x equals to 2, that value of x which made the value of this polynomial equal to zero is called the zero of the polynomial. And for a second, if you would like to see this on the graph, let's draw the coordinate axis. So this y axis would represent the values of this polynomial f of x. This x axis would represent the values of the input variable. And the graph of this polynomial would be a straight line, something like this. And this point here would represent the zero of this polynomial x minus 2, because the y coordinate of this point is equal to zero. The value of the polynomial is zero. So for this corresponding x value, that is x equals to 2, the value of the polynomial is zero, hence this is the zero of the polynomial. Having said that, now let us come back to the graph that we actually have here. So the question is, what are those points where p of x is equal to zero? In other words, what are those points where the graph of the polynomial p of x intersects or touches the x axis? Because for those points, the y coordinate will be zero and hence those x coordinates would be our zeros of the polynomial. Let us mark those points here. For example, this point here, this point, this point as well, again this point here and this point. For these points, the y coordinate is zero, because all these points lie on the x axis. And how many such points do we have here? 1, 2, 3, 4 and 5. So number of zeros for this polynomial p of x would be equal to 5.