If the roots of a quadratic equation are real and unequal, which one of the following is necessarily true?

Options

A. `Dlt0`
B. D = 0
C. `Dgt0`
D. `Dge0`

Answer

To determine the condition under which the roots of a quadratic equation are real and unequal, we need to analyze the discriminant (D) of the quadratic equation. The general form of a quadratic equation is:

\[ ax^2 + bx + c = 0 \]

### Step-by-Step Solution:

1. **Identify the Discriminant**:
The discriminant (D) of a quadratic equation is given by the formula:
\[ D = b^2 - 4ac \]

2. **Condition for Real and Unequal Roots**:
For the roots of the quadratic equation to be real and unequal, the discriminant must be greater than zero:
\[ D > 0 \]

3. **Conclusion**:
Therefore, if the roots of a quadratic equation are real and unequal, it is necessarily true that:
\[ b^2 - 4ac > 0 \]

### Final Answer:
The correct statement is that the discriminant \( D \) must be greater than 0.

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