What will be number of zeros of the polynomials whose graphs are either touching or intersecting the axis only at the points :
`(i) (3,0)`, `(0,2)` & `(3,0)` `(ii) (0,4)`, `(0,0)` and `(0,-4)`

Answer

To find the number of zeros of the given polynomials based on their graphs touching or intersecting the x-axis at specified points, we will analyze each case step by step.

### Part (i): Points (3,0), (0,2), and (3,0)

1. **Identify the points**: The points given are (3,0), (0,2), and (3,0).
- The point (3,0) indicates that the polynomial intersects the x-axis at x = 3.
- The point (0,2) indicates that the polynomial does not intersect the x-axis at this point since the y-coordinate is not zero.
- The point (3,0) is repeated.

2. **Determine the zeros**:
- The only relevant point for finding zeros is (3,0) since it is the only point where the polynomial intersects the x-axis.
- The point (3,0) counts as one zero. The repeated occurrence of (3,0) does not add to the count of distinct zeros.

3. **Conclusion for Part (i)**:
- There is only **1 zero** for the polynomial based on the given points.

### Part (ii): Points (0,4), (0,0), and (0,-4)

1. **Identify the points**: The points given are (0,4), (0,0), and (0,-4).
- The point (0,0) indicates that the polynomial intersects the x-axis at x = 0.
- The points (0,4) and (0,-4) do not intersect the x-axis since their y-coordinates are not zero.

2. **Determine the zeros**:
- The only relevant point for finding zeros is (0,0) since it is the only point where the polynomial intersects the x-axis.
- Thus, (0,0) counts as one zero.

3. **Conclusion for Part (ii)**:
- There is only **1 zero** for the polynomial based on the given points.

### Final Answers:
- For part (i), the number of zeros is **1**.
- For part (ii), the number of zeros is **1**.

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