Which one of the following is not a quadratic equation?
Show Hint
- \( (x + 2)^2 = 2(x + 3) \)
- \( x^2 + 3x = (-1)(1 - 3x)^2 \)
- \( x^3 - 2x^2 + 2x + 1 = (x + 1)^3 \)
- \( (x + 2)(x - 1) = x^2 - 2x - 3 \)
The Correct Option is D
Solution and Explanation
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.
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