Question 1
The graph of a polynomial p(x) is shown. Find the number of zeroes of the polynomial.
(Assume the graph cuts the x-axis exactly once.)
Step 1: Zeroes of a polynomial are the x-coordinates where the graph cuts the x-axis.
Step 2: From the given graph, the curve intersects the x-axis at exactly one point.
Step 3: Hence, the polynomial has exactly 1 zero.
Answer: Number of zeroes = 1
Question 2
A graph of a polynomial intersects the x-axis at two distinct points. Find the number of zeroes.
Step 1: Zeroes are the x-coordinates where the graph touches or cuts the x-axis.
Step 2: The graph cuts the x-axis at two different points.
Conclusion: Each intersection gives one zero.
Answer: Number of zeroes = 2
Question 3
The graph of a polynomial touches the x-axis at exactly one point. Find the number of zeroes.
Step 1: When a curve only touches the x-axis, both intersection points coincide.
Step 2: This means there is only one real zero.
Answer: Number of zeroes = 1
Question 4
The graph of a polynomial does not intersect the x-axis at any point. Find the number of zeroes.
Step 1: Zeroes exist only where the graph meets the x-axis.
Step 2: Since the graph does not touch or cut the x-axis, there are no real zeroes.
Answer: Number of zeroes = 0
Question 5
A polynomial graph cuts the x-axis at three different points. How many zeroes does it have?
Step 1: Each intersection with x-axis gives one zero.
Step 2: Since the curve cuts the x-axis at three distinct points, it has three zeroes.
Answer: Number of zeroes = 3