MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 27

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerPolynomials

Find a quadratic polynomial whose sum and product of zeroes are 0 and $- 9$ , respectively. Also, find the zeroes of the polynomial so obtained.

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

Hints

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

Hint 1

Recall the form $x^{2} - (sum) x + (product)$ .

Hint 2

The polynomial you get is a difference of two squares.

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.

A quadratic polynomial with sum of zeroes S and product P is $x^{2} - S x + P$ . So the polynomial is $x^{2} - 0 \cdot x + (- 9) = x^{2} - 9$ .
1 mark
For the zeroes: $x^{2} - 9 = (x + 3) (x - 3) = 0$ .
1 mark
Zeroes are $x = - 3$ and $x = 3$ . Check: sum $= 0$ and product $= - 9$ .
1 mark

Answer: x² − 9; zeroes −3 and 3

Where the marks are

Forms the polynomial $x^{2} - 9$ (1 mark)
Factorises it as $(x + 3) (x - 3)$ (1 mark)
States the zeroes $- 3, 3$ (1 mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/1/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2025: question 27

Hints

Step-by-step solution

Revise the chapter

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