Which of the following equations is a quadratic equation ? (A) x² = (x+1)² (B) (x-1)(x+2) = 2x + 1 (C) (x+2)³ = 2x(x² - 1) (D) √(x) = x²

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 5

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 1 mark · MCQQuadratic Equations

Which of the following equations is a quadratic equation ?

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

Expand and simplify each equation.

Hint 2

Check whether the highest power of x left after simplifying is exactly 2.

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.

(B): $x^{2} + x - 2 = 2 x + 1 \Rightarrow x^{2} - x - 3 = 0$ , which has degree 2, so it is quadratic.
1 mark
(A) reduces to $2 x + 1 = 0$ , which is linear. (C) has degree 3, since the $x^{3}$ terms do not cancel. (D) is not a polynomial equation because of $x$ . So the answer is option (B).

Answer: Option (B)

Where the marks are

Simplifies (B) to $x^{2} - x - 3 = 0$ and identifies it as quadratic (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 paper2025 board paper, set 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 5

Hints

Step-by-step solution

Revise the chapter

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