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

CBSE Class 10 Mathematics Basic 2025: question 27

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, 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 the zeroes of the polynomial $9 s^{2} - 6 s + 1$ and verify the relationship between the zeroes and the coefficients of the given polynomial.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

The polynomial is a perfect square. Compare it with $(a - b)^{2}$ .

Hint 2

Compare the sum and product of the zeroes with −b/a and c/a, where a = 9, b = −6, c = 1.

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.

$9 s^{2} - 6 s + 1 = (3 s)^{2} - 2 (3 s) (1) + 1^{2} = (3 s - 1) (3 s - 1)$ . So the zeroes are $\frac{1}{3}$ and $\frac{1}{3}$ .
1 mark
Sum of zeroes $= \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ and $\frac{- ( coefficient of s )}{coefficient of s ^{2}} = \frac{- ( - 6 )}{9} = \frac{2}{3}$ . These are equal, so the sum relation is verified.
1 mark
Product of zeroes $= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$ and $\frac{constant term}{coefficient of s ^{2}} = \frac{1}{9}$ . These are equal, so the product relation is verified.
1 mark

Answer: Zeroes: 1/3, 1/3; sum = 2/3 = −b/a, product = 1/9 = c/a (verified)

Where the marks are

Factorises the polynomial and finds both zeroes as 1/3 (1 mark)
Verifies sum of zeroes = −b/a (1 mark)
Verifies product of zeroes = c/a (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 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 27

Hints

Step-by-step solution

Revise the chapter

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