The sum and product of zeroes of a quadratic polynomial p(x) are (-1)/(3) and 2 respectively. The polynomial p(x) is : (A) 3x² - x + 6 (B) x² + 1/3x - 2 (C) 3x² - x + 2 (D) -3x² - x - 6

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 14

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQPolynomials

The sum and product of zeroes of a quadratic polynomial p(x) are $\frac{- 1}{3}$ and 2 respectively. The polynomial p(x) is :

(A) $3 x^{2} - x + 6$
(B) $x^{2} + \frac{1}{3} x - 2$
(C) $3 x^{2} - x + 2$
(D) $- 3 x^{2} - x - 6$

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

A quadratic with given zeroes is $k [x^{2} - (sum) x + product]$ .

Hint 2

For each option, check $- b / a$ and $c / a$ .

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.

$p (x) = k [x^{2} - (sum) x + product] = k (x^{2} + \frac{1}{3} x + 2)$ .
Taking $k = - 3$ gives $- 3 x^{2} - x - 6$ . Check: sum $= - \frac{- 1}{- 3} = - \frac{1}{3}$ and product $= \frac{- 6}{- 3} = 2$ . The answer is option (D).
1 mark

Answer: $- 3 x^{2} - x - 6$ ; option (D)

Where the marks are

Chooses option (D) $- 3 x^{2} - x - 6$ (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 paper2026 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 14

Hints

Step-by-step solution

Revise the chapter

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