Which of the following is not a quadratic equation

Options

A. `2x (x +4) - 11 =x (x-3) + 6`
B. `4x (x +4) - 11= 5x (x -3) + 5`
C. `x (x +2) - 15 = x (x-5) + 11`
D. `2x ^(2) + 8x - 11=0`

Answer

To determine which of the following options is not a quadratic equation, we need to analyze each equation based on the standard form of a quadratic equation, which is:

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

where \( a \neq 0 \) and the degree of the polynomial is 2.

### Step-by-Step Solution:

1. **Identify the Options**: We need to check each option provided to see if it fits the criteria of a quadratic equation.

2. **Check Option A**:
- Given: \( 2x^2 + 8x - 11 = x^2 - 3x + 6 \)
- Rearranging gives: \( 2x^2 + 8x - 11 - x^2 + 3x - 6 = 0 \)
- Simplifying: \( (2x^2 - x^2) + (8x + 3x) - (11 + 6) = 0 \)
- Result: \( x^2 + 11x - 17 = 0 \)
- This is a quadratic equation.

3. **Check Option B**:
- Given: \( 4x^2 + 16x + 8x + 3 - 11 = 5x^2 - 15x + 5 \)
- Rearranging gives: \( 4x^2 + 24x - 8 - 5x^2 + 15x - 5 = 0 \)
- Simplifying: \( (4x^2 - 5x^2) + (24x + 15x) - (8 + 5) = 0 \)
- Result: \( -x^2 + 39x - 13 = 0 \)
- This is a quadratic equation.

4. **Check Option C**:
- Given: \( x^2 + 2x - 15 = x^2 - 5x + 11 \)
- Rearranging gives: \( x^2 + 2x - 15 - x^2 + 5x - 11 = 0 \)
- Simplifying: \( (x^2 - x^2) + (2x + 5x) - (15 + 11) = 0 \)
- Result: \( 7x - 26 = 0 \)
- This is a linear equation, not a quadratic equation (degree is 1).

5. **Check Option D**:
- Given: \( x^2 + 4x + 4 = 0 \)
- This is already in the standard form of a quadratic equation.
- Therefore, it is a quadratic equation.

### Conclusion:
After checking all options, we find that **Option C** is not a quadratic equation.

### Final Answer:
**Option C is not a quadratic equation.**

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