If the quadratic graph opens downward, then the roots are always

Options

A. imagiriaiy
B. real
C. equal
D. cannot be determined

Answer

To solve the question, "If the quadratic graph opens downward, then the roots are always," we need to analyze the characteristics of a quadratic equation based on its graph.

### Step-by-Step Solution:

1. **Understanding the Quadratic Graph**:
A quadratic graph is represented by the equation \( ax^2 + bx + c = 0 \). The sign of \( a \) determines the direction of the graph. If \( a < 0 \), the graph opens downward.

2. **Analyzing the Roots**:
The roots of a quadratic equation can be determined by the discriminant \( D \), which is given by the formula:
\[ D = b^2 - 4ac \]
The nature of the roots depends on the value of \( D \):
- If \( D > 0 \): There are two distinct real roots.
- If \( D = 0 \): There is one real root (the roots are equal).
- If \( D < 0 \): There are no real roots (the roots are imaginary).

3. **Considering the Graph Opening Downward**:
Since the graph opens downward, we can have three scenarios:
- The graph intersects the x-axis at two points (two distinct real roots).
- The graph touches the x-axis at one point (one real root).
- The graph does not intersect the x-axis at all (no real roots, only imaginary roots).

4. **Conclusion**:
Therefore, when the quadratic graph opens downward, the roots can be real (either distinct or equal) or imaginary. Since the question asks what the roots are "always," we can conclude that it is not possible to determine a single type of root. The correct answer is that the roots "cannot be determined" without additional information about the coefficients \( a, b, \) and \( c \).

### Final Answer:
The roots are always "cannot be determined."