Find the zeroes of the polynomial p(x) = x² + 4/3x - 4/3.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 22

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerPolynomials

Find the zeroes of the polynomial $p (x) = x^{2} + \frac{4}{3} x - \frac{4}{3}$ .

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

Hints

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

Hint 1

Take $\frac{1}{3}$ common to remove the fractions.

Hint 2

Factorise $3 x^{2} + 4 x - 4$ by splitting $4 x$ into two terms whose product is $- 12 x^{2}$ .

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.

$p (x) = x^{2} + \frac{4}{3} x - \frac{4}{3} = \frac{1}{3} (3 x^{2} + 4 x - 4)$
½ mark
Split the middle term: $= \frac{1}{3} (3 x^{2} + 6 x - 2 x - 4)$
½ mark
$= \frac{1}{3} [3 x (x + 2) - 2 (x + 2)] = \frac{1}{3} (3 x - 2) (x + 2)$
½ mark
$p (x) = 0 \Rightarrow x = \frac{2}{3}$ or $x = - 2$ . The zeroes are $\frac{2}{3}$ and $- 2$ .
½ mark

Answer: $\frac{2}{3}$ and $- 2$

Where the marks are

Takes $\frac{1}{3}$ common to get $3 x^{2} + 4 x - 4$ (½ mark)
Splits the middle term correctly (½ mark)
Factorises as $(3 x - 2) (x + 2)$ (½ mark)
States zeroes $\frac{2}{3}, - 2$ (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 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 22

Hints

Step-by-step solution

Revise the chapter

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