If the roots of a quadratic equation are unequal, which one of the following cannot be true?

Options

A. A)`Dgt0`
B. B)`Dlt0`
C. C)D = 0
D. D)Roots are conjugate also

Answer

To determine which condition cannot be true if the roots of a quadratic equation are unequal, we start by recalling the standard form of a quadratic equation:

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

### Step 1: Understand the condition for unequal roots
The roots of the quadratic equation can be found using the discriminant \( D \), which is given by:

\[ D = b^2 - 4ac \]

For the roots to be unequal, the discriminant must be greater than zero:

\[ D > 0 \]

### Step 2: Analyze the options
Now, let's analyze the options given in the question:

1. **Option A**: \( D \neq 0 \)
- This condition is true for unequal roots since \( D \) must be greater than zero.

2. **Option B**: \( D < 0 \)
- This condition is false for unequal roots because if \( D < 0 \), the roots are complex and not real, hence they cannot be unequal in the real number sense.

3. **Option C**: \( D = 0 \)
- This condition is also false for unequal roots because if \( D = 0 \), the roots are equal.

4. **Option D**: \( D > 0 \)
- This condition is true for unequal roots since it confirms that the roots are distinct.

### Step 3: Conclusion
From the analysis, we can conclude that the condition that cannot be true if the roots are unequal is:

**Option C**: \( D = 0 \)

### Final Answer
Thus, the answer is **Option C**: \( D = 0 \).

---