Which of the following is quadratic equation ?

Options

A. `x^(3)-2x^(2)-sqrt(5)-x=0`
B. `3x^(2)-5x+9=x^(2)-7x+3`
C. `((x+1)/x)^(2)=3((x+1)/(x+4))`
D. `x^(3)+x+36`

Answer

To determine which of the given options is a quadratic equation, we need to identify the equations and check their degrees. A quadratic equation is defined as an equation of the form \( Ax^2 + Bx + C = 0 \), where \( A, B, \) and \( C \) are real numbers, and the highest degree of the variable \( x \) is 2.

### Step-by-Step Solution:

1. **Identify the Options**:
We need to analyze each option provided to see if they fit the form of a quadratic equation.

2. **Check the First Option**:
Let's assume the first option is \( x^3 - 2x^2 = 0 \).
- The highest power of \( x \) here is 3 (from \( x^3 \)).
- Since the degree is 3, this is a **cubic equation**, not a quadratic equation.

3. **Check the Second Option**:
Assume the second option is \( 3x^2 - 5x + 9 = x^2 - 7x + 3 \).
- Rearranging gives us \( 3x^2 - x^2 - 5x + 7x + 9 - 3 = 0 \).
- This simplifies to \( 2x^2 + 2x + 6 = 0 \).
- The highest power of \( x \) here is 2.
- Since the degree is 2, this is a **quadratic equation**.

4. **Check the Third Option**:
Assume the third option is \( \frac{x + 1}{x^2} = \frac{3}{x + 4} \).
- Cross-multiplying gives \( (x + 1)(x + 4) = 3x^2 \).
- Expanding gives \( x^2 + 5x + 4 = 3x^2 \).
- Rearranging gives \( -2x^2 + 5x + 4 = 0 \).
- The highest power of \( x \) here is also 2.
- Since the degree is 2, this is another **quadratic equation**.

5. **Check the Fourth Option**:
Assume the fourth option is \( x^3 + x + 1 = 0 \).
- The highest power of \( x \) here is 3.
- Since the degree is 3, this is a **cubic equation**, not a quadratic equation.

### Conclusion:
The second and third options are quadratic equations, while the first and fourth options are cubic equations.

### Final Answer:
- The quadratic equations are found in the **second and third options**.