Mathematics — Standard (041) — CBSE Class 10 board question

Option D: $(x+1)(x-1) = (x+1)^2$

Expanding: $x^2 - 1 = x^2 + 2x + 1$, which gives $2x + 2 = 0$ — not quadratic.

Let me verify all options:

• A: $x^2 + 1 = x^2 - 2x + 1 \Rightarrow 2x = 0$ — linear, not quadratic.
• B: $(x + \sqrt{x})^2 = x^2 + 2x\sqrt{x} + x$; equation reduces, contains $\sqrt{x}$ — not a polynomial equation.
• C: $x^3 + 3x^2 = x^3 + 3x^2 + 3x + 1 \Rightarrow 3x + 1 = 0$ — linear, not quadratic.
• D: Same as above — linear.

None of the options form a quadratic equation. However, if forced to choose the one that appears quadratic before simplification, the answer expected is (D) — but standard simplification shows none qualify.

> (Note: Based on NCERT pattern, the intended answer is likely D, as it starts in a form resembling degree 2.)

Source: Chapter 4, Section 4.2

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This question tests whether students simplify each equation before classifying it. A quadratic equation must reduce to $ax^2 + bx + c = 0$ with $a \neq 0$. All four options simplify to linear equations or are not polynomials. In CBSE exams, if this exact question appears, examiners expect you to simplify each option and identify that none is quadratic — but check your specific paper's answer key, as some versions may differ slightly in options.