If the graph intersects X-axis at two distinct points, then,the roots are necessarily

Options

A. complex
B. irrational
C. rational
D. real

Answer

To solve the question, we need to analyze the implications of a graph intersecting the X-axis at two distinct points.

### Step-by-Step Solution:

1. **Understanding the Graph**:
- The graph of a polynomial function intersects the X-axis at points where the function equals zero. These points represent the roots of the polynomial.

2. **Identifying the Nature of Roots**:
- If the graph intersects the X-axis at two distinct points, it indicates that there are two solutions (or roots) to the equation represented by the graph.

3. **Types of Roots**:
- Roots can be classified as:
- Real: These are the roots that can be plotted on the number line.
- Complex: These roots involve imaginary numbers and do not intersect the X-axis.
- Rational: These are real roots that can be expressed as a fraction.
- Irrational: These are real roots that cannot be expressed as a fraction.

4. **Analyzing the Given Condition**:
- Since the graph intersects the X-axis at two distinct points, it implies that both roots are real numbers. This is because complex roots would not intersect the X-axis at all.

5. **Conclusion**:
- Therefore, if the graph intersects the X-axis at two distinct points, the roots are necessarily real.

### Final Answer:
The roots are necessarily **real**.