CBSE · Class 10 · Mathematics · Quadratic EquationsWhich of the following is a quadratic equation?
Step-by-Step Solution
Expanding option B: $(x + 1)^2 = 2(x - 3) \Rightarrow x^2 + 2x + 1 = 2x - 6 \Rightarrow x^2 + 7 = 0$, which is of the form $ax^2 + bx + c = 0$ with $a \neq 0$. Hence, it is a quadratic equation.
Detailed Options Breakdown
Option : $x^2 + 2x + 1 = (x - 1)^2$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
Option 1: $(x + 1)^2 = 2(x - 3)$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $(x + 2)(x + 1) = x^2 - 1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
Option 3: $x^3 - x^2 = (x - 1)^3$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
💡 Study Guide: This question tests core syllabus concepts from Quadratic Equations. For formulas, key summaries, and mock exam reference guides, read the full Quadratic Equations Revision Notes.