In the graph, you can see that the graph of y = 2x+3 intersects the X-axis between x = –1 and x = –2, that is,at the point (-3/2 0). But x = -3/2 is the zero of the polynomial 2x + 3. Thus, the zero of the polynomial 2x + 3 is the x-coordinate of the point where the graph of y = 2x + 3 intersects the X-axis.

In general, for a linear polynomial ax + b, a not equal to 0 , the graph of y = ax + b is a straight line which intersects the X-axis at exactly one point, namely, (-b/a ,0)

Therefore, the linear polynomial ax + b, a not equal to 0, has exactly one zero, namely, the x-coordinate of the point where the graph of y = ax + b intersects the X-axis.

Now, let us look for the geometrical meaning of a zero of a quadratic polynomial. Consider the quadratic polynomial x² – 3x – 4. Let us see how the graph of y = x² – 3x – 4 looks like. Let us list a few values of y = x²– 3x – 4 corresponding to a few values for x as given in Table 3.2.