MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 29

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerQuadratic Equations

Find two consecutive negative integers, sum of whose squares is 481.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

Let the integers be x and x + 1 and write the sum of their squares.

Hint 2

You get a quadratic. Look for two numbers with product −240 and difference 1, and keep only the root that gives negative integers.

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.

Let the two consecutive negative integers be $x$ and $x + 1$ .
Given: $x^{2} + (x + 1)^{2} = 481$
1 mark
$2 x^{2} + 2 x + 1 = 481 \Rightarrow 2 x^{2} + 2 x - 480 = 0 \Rightarrow x^{2} + x - 240 = 0$
½ mark
Splitting the middle term: $x^{2} + 16 x - 15 x - 240 = 0$
$\Rightarrow (x + 16) (x - 15) = 0 \Rightarrow x = - 16$ or $x = 15$
1 mark
The integers must be negative, so $x = 15$ is rejected and $x = - 16$ .
Required integers: $- 16$ and $- 15$ .
(Check: $256 + 225 = 481$ .)
½ mark

Answer: −16 and −15

Where the marks are

Forms the equation $x^{2} + (x + 1)^{2} = 481$ (1 mark)
Reduces it to $x^{2} + x - 240 = 0$ (½ mark)
Factorises to get x = −16 or 15 (1 mark)
Rejects 15 and states the integers −16, −15 (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 29

Hints

Step-by-step solution

Revise the chapter

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