The graph of y = p(x) is given, for a polynomial p(x). The number of zeroes of p(x) from the graph is

Options:

(a) 3

(b) 1

(c) 2

(d) 0

• The number of zeroes of a polynomial refers to the number of times the polynomial intersects the x-axis. In other words, it’s the number of solutions to the equation p(x) = 0.

By looking at the graph of the polynomial, we can see that it intersects the x-axis only once. This intersection point is located around x = -2.5.

Therefore, the number of zeroes of the polynomial p(x) is 1, which corresponds to option B.

The other options can be eliminated as follows:

• Option A (3): The graph intersects the x-axis only once, not three times.
• Option C (2): The graph intersects the x-axis only once, not twice.
• Option D (0): The graph intersects the x-axis once, not zero times.

In conclusion, based on the graph of the polynomial, option B (1) is the correct answer as it represents the number of times the polynomial intersects the x-axis.