Find the zeroes of the polynomial p(x) = 3x² - 4x - 4. Hence, write a polynomial whose each of the zeroes is 2 more than zeroes of p(x).

Zeroes -2/3, 2; polynomial 3x² - 16x + 16

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 27

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, 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 $p (x) = 3 x^{2} - 4 x - 4$ . Hence, write a polynomial whose each of the zeroes is 2 more than zeroes of $p (x)$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Split the middle term: find two numbers with product $- 12$ and sum $- 4$ .

Hint 2

Add 2 to each zero, then use $x^{2} - (sum) x + product$ .

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.

$3 x^{2} - 4 x - 4 = 3 x^{2} - 6 x + 2 x - 4 = (3 x + 2) (x - 2)$ , so the zeroes are $- \frac{2}{3}$ and $2$ .
1 mark
New zeroes (each 2 more): $- \frac{2}{3} + 2 = \frac{4}{3}$ and $2 + 2 = 4$ .
½ mark
Sum of new zeroes $= \frac{4}{3} + 4 = \frac{16}{3}$
½ mark
Product of new zeroes $= \frac{4}{3} \times 4 = \frac{16}{3}$
½ mark
Required polynomial $= x^{2} - \frac{16}{3} x + \frac{16}{3}$ , i.e. $3 x^{2} - 16 x + 16$ (or any $k (3 x^{2} - 16 x + 16)$ ).
½ mark

Answer: Zeroes $- \frac{2}{3}, 2$ ; polynomial $3 x^{2} - 16 x + 16$

Where the marks are

Finds zeroes $- 2/3$ and $2$ (1 mark)
New zeroes $4/3$ and $4$ (½ mark)
Sum $16/3$ (½ mark)
Product $16/3$ (½ mark)
Writes polynomial $3 x^{2} - 16 x + 16$ (½ mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Forming a Quadratic Polynomial from Its Zeros

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 30/6/1 (Standard): 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 Standard 2025: question 27

Hints

Step-by-step solution

Revise the chapter

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