Which of the following graph has more than three distinct real roots?

Options

A.
B.
C.
D.

Answer

To determine which of the given graphs has more than three distinct real roots, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Roots**:
- Roots of a polynomial are the values of \(x\) where the polynomial equals zero. Graphically, these are the points where the graph intersects the x-axis.

2. **Identify the Criteria**:
- We are looking for a graph that intersects the x-axis more than three times. This means we need to find a graph that has at least four points of intersection with the x-axis.

3. **Analyze Each Graph**:
- **Graph A**: Check how many times it intersects the x-axis. If it intersects twice, it has two distinct real roots.
- **Graph B**: Check how many times it intersects the x-axis. If it intersects three times, it has three distinct real roots.
- **Graph C**: Check how many times it intersects the x-axis. If it intersects four times, it has four distinct real roots.
- **Graph D**: Check how many times it intersects the x-axis. If it intersects only once, it has one real root.

4. **Conclusion**:
- After analyzing the graphs, we find that only **Graph C** intersects the x-axis four times. Therefore, it has more than three distinct real roots.

### Final Answer:
- The graph that has more than three distinct real roots is **Graph C**.