Question

Which one of the following is not a quadratic equation?

• A. \( (x + 2)^2 = 2(x + 3) \)
• B. \( x^2 + 3x = (-1)(1 - 3x)^2 \)
• C. \( x^3 - 2x^2 + 2x + 1 = (x + 1)^3 \)
• D. \( (x + 2)(x - 1) = x^2 - 2x - 3 \)

Hint:

A quadratic equation always has the highest degree of 2. If the highest power of \( x \) is 3 or higher, it is not quadratic.

Answer 1

The Correct Option is D

A quadratic equation is an equation of degree 2, which means the highest power of the variable \( x \) is 2. 
Step 1: Option (1) \( (x + 2)^2 = 2(x + 3) \) is a quadratic equation as it simplifies to a degree 2 equation. 
Step 2: Option (2) \( x^2 + 3x = (-1)(1 - 3x)^2 \) simplifies to a quadratic equation upon expansion. 
Step 3: Option (3) \( (x + 2)(x - 1) = x^2 - 2x - 3 \) is also a quadratic equation. 
Step 4: Option (4) \( x^3 - 2x^2 + 2x + 1 = (x + 1)^3 \) is a cubic equation, as the highest degree is 3. 
Thus, the correct answer is option (4), as it is not a quadratic equation.