Find the zeroes of the polynomial p(x) = 3x² + 7x - 20 and verify the relationship between its zeroes and the coefficients.

Zeroes -4 and 53; sum -73, product -20/3 (verified)

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 30(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section C, question 30(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(b) · 3 marks · Short answerPolynomials

Find the zeroes of the polynomial $p (x) = 3 x^{2} + 7 x - 20$ and verify the relationship between its zeroes and the coefficients.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

Split the middle term: find two numbers with product $3 \times (- 20) = - 60$ and sum 7.

Hint 2

Compare the sum and product of the zeroes with $- \frac{b}{a}$ and $\frac{c}{a}$ .

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.

$3 x^{2} + 7 x - 20 = 3 x^{2} + 12 x - 5 x - 20 = 3 x (x + 4) - 5 (x + 4) = (3 x - 5) (x + 4)$ . Zeroes: $x = \frac{5}{3}$ and $x = - 4$ .
1 mark
Sum of zeroes $= - 4 + \frac{5}{3} = - \frac{7}{3}$ , and $- \frac{coefficient of x}{coefficient of x ^{2}} = - \frac{7}{3}$ . Verified.
1 mark
Product of zeroes $= - 4 \times \frac{5}{3} = - \frac{20}{3}$ , and $\frac{constant term}{coefficient of x ^{2}} = \frac{- 20}{3}$ . Verified.
1 mark

Answer: Zeroes $- 4$ and $\frac{5}{3}$ ; sum $- \frac{7}{3}$ , product $- \frac{20}{3}$ (verified)

Where the marks are

Finds zeroes $- 4, \frac{5}{3}$ (1 mark)
Verifies sum relation (1 mark)
Verifies product relation (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 430/5/1 (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 2026: question 30(b)

Hints

Step-by-step solution

Revise the chapter

More questions from Polynomials