Which one of the following is not a quadratic equation? (A) (x+2)² = 2(x+3) (B) x² + 3x = (-1)(1-3x)² (C) x³ - x² + 2x + 1 = (x+1)³ (D) (x+2)(x+1) = x² + 2x + 3

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 6

From the official CBSE sample question paper for 2025-26, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQQuadratic Equations

Which one of the following is not a quadratic equation?

(A) $(x + 2)^{2} = 2 (x + 3)$
(B) $x^{2} + 3 x = (- 1) (1 - 3 x)^{2}$
(C) $x^{3} - x^{2} + 2 x + 1 = (x + 1)^{3}$
(D) $(x + 2) (x + 1) = x^{2} + 2 x + 3$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

Expand both sides of each equation and bring all terms to one side.

Hint 2

Look for the equation in which the $x^{2}$ terms cancel out.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Simplify each option. (A) $x^{2} + 4 x + 4 = 2 x + 6$ gives $x^{2} + 2 x - 2 = 0$ , which is quadratic. (B) $x^{2} + 3 x = - (1 - 6 x + 9 x^{2})$ gives $10 x^{2} - 3 x + 1 = 0$ , which is quadratic. (C) $x^{3} - x^{2} + 2 x + 1 = x^{3} + 3 x^{2} + 3 x + 1$ gives $4 x^{2} + x = 0$ , which is quadratic.
(D) $x^{2} + 3 x + 2 = x^{2} + 2 x + 3$ gives $x - 1 = 0$ . This has degree 1, so it is not a quadratic equation. The answer is option (D).
1 mark

Answer: Option (D)

Where the marks are

Simplifies (D) to the linear equation $x - 1 = 0$ and concludes it is not quadratic, option (D) (1 mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Standard Form of a Quadratic Equation

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2025-26: question 6

Hints

Step-by-step solution

Revise the chapter

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