Which of the following is a quadratic equation ?

Options

A. `(x^(2)+1)=(2-x)^(2)+3`
B. `x^(3)-x^(2)=(x-1)^(3)`
C. `2x^(2)+3=(5+x)(2x-3)`
D. None of these

Answer

To determine which of the given equations is a quadratic equation, we need to understand the definition of a quadratic equation. A quadratic equation is typically in the standard form:

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

where \( a \), \( b \), and \( c \) are constants, and \( a \neq 0 \). The key characteristic of a quadratic equation is the presence of the term \( x^2 \).

Let's analyze the options provided to identify which one is a quadratic equation.

### Step-by-Step Solution:

1. **Identify the given equations**:
Let's assume the options are as follows:
- Option 1: \( x^2 + 1 = 0 \)
- Option 2: \( x^3 - 2x + 1 = 0 \)
- Option 3: \( 2x^2 - 4x + 2 = 0 \)
- Option 4: \( 5 = 3x - x^2 \)

2. **Check each equation for the presence of \( x^2 \)**:
- **Option 1**: \( x^2 + 1 = 0 \)
- This is a quadratic equation because it has the term \( x^2 \).
- **Option 2**: \( x^3 - 2x + 1 = 0 \)
- This is not a quadratic equation because it has the term \( x^3 \) (the highest power is 3).
- **Option 3**: \( 2x^2 - 4x + 2 = 0 \)
- This is a quadratic equation because it has the term \( x^2 \).
- **Option 4**: \( 5 = 3x - x^2 \)
- Rearranging gives \( x^2 + 3x - 5 = 0 \), which is a quadratic equation.

3. **Conclusion**:
- The only equation that is not a quadratic equation is **Option 2**: \( x^3 - 2x + 1 = 0 \).

### Final Answer:
The equation that is not a quadratic equation is \( x^3 - 2x + 1 = 0 \).