Find zeroes of the polynomial 6x² - 7x - 3 and verify the relationship between zeroes and its coefficients.

Zeroes 3/2 and -1/3; sum = 7/6, product = -1/2, relations verified.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 26(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section C, question 26(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(b) · 3 marks · Short answerPolynomials

Find zeroes of the polynomial $6 x^{2} - 7 x - 3$ and verify the relationship between zeroes and its coefficients.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

Look for two numbers whose product is $6 \times (- 3) = - 18$ and whose sum is $- 7$ .

Hint 2

After finding the zeroes, compare their sum with $- \frac{b}{a}$ and their product with $\frac{c}{a}$ .

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.

Split the middle term: $6 x^{2} - 7 x - 3 = 6 x^{2} - 9 x + 2 x - 3 = 3 x (2 x - 3) + 1 (2 x - 3) = (2 x - 3) (3 x + 1)$ .
Zeroes: $x = \frac{3}{2}$ and $x = - \frac{1}{3}$ .
1 mark
Sum of zeroes $= \frac{3}{2} - \frac{1}{3} = \frac{7}{6}$ , and $- \frac{coefficient of x}{coefficient of x ^{2}} = - \frac{- 7}{6} = \frac{7}{6}$ . Verified.
1 mark
Product of zeroes $= \frac{3}{2} \times (- \frac{1}{3}) = - \frac{1}{2}$ , and $\frac{constant term}{coefficient of x ^{2}} = \frac{- 3}{6} = - \frac{1}{2}$ . Verified.
1 mark

Answer: Zeroes $\frac{3}{2}$ and $- \frac{1}{3}$ ; sum $= \frac{7}{6}$ , product $= - \frac{1}{2}$ , relations verified.

Where the marks are

Factorises and finds zeroes $\frac{3}{2}, - \frac{1}{3}$ (1 mark)
Verifies sum of zeroes $= - \frac{b}{a} = \frac{7}{6}$ (1 mark)
Verifies product of zeroes $= \frac{c}{a} = - \frac{1}{2}$ (1 mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Relationship Between Zeros and Coefficients

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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 26(b)

Hints

Step-by-step solution

Revise the chapter

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