Which of the following is not a quadratic equation? (A) 2(x-1)² = 4x² - 2x + 1 (B) 2x - x² = x² + 5 (C) (√(2)x + √(3))² + x² = 3x² - 5x (D) (x² + 2x)² = x^4 + 3 + 4x³

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 16

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQQuadratic Equations

Which of the following is not a quadratic equation?

(A) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(B) $2 x - x^{2} = x^{2} + 5$
(C) $(2 x + 3)^{2} + x^{2} = 3 x^{2} - 5 x$
(D) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Expand each equation and bring all terms to one side.

Hint 2

Look for the option 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.

For (C): $2 x^{2} + 26 x + 3 + x^{2} = 3 x^{2} - 5 x$ , which simplifies to $(26 + 5) x + 3 = 0$ . The $x^{2}$ terms cancel, so it is linear, not quadratic.
Each of the other options keeps an $x^{2}$ term with highest degree 2 after simplifying. Answer: option (C).
1 mark

Answer: Option (C)

Where the marks are

Expands (C) and shows the $x^{2}$ terms cancel (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 paper2023 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 16

Hints

Step-by-step solution

Revise the chapter

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