Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x).

The graph intersects the x-axis at two points. Hence, the polynomial p(x) has 2 zeroes.

NCERT Class X Chapter 2: Polynomials Example 1(ii)

The graph of the polynomial $ y = p(x) $ is given.

The number of zeroes of the polynomial $ p(x) $.

Number of zeroes of a polynomial = Number of points where the graph of the polynomial intersects the x-axis.

Step 1: Observe the given graph of the polynomial.

$$ y = p(x) $$

Step 2: Identify the points where the graph intersects the x-axis.

Step 3: The graph cuts the x-axis at two distinct points.

Step 4: Each point of intersection with the x-axis represents one zero of the polynomial.

The number of zeroes of the polynomial $ p(x) $ is 2.