Find the zeroes of the polynomial p(x) = 6x² + 13x - 5 and verify the relationship between its zeroes and the coefficients.

Zeroes 13 and -52; sum = -13/6, product = -56 (relationship verified)

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 26

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerPolynomials

Find the zeroes of the polynomial $p (x) = 6 x^{2} + 13 x - 5$ and verify the relationship between its zeroes and the coefficients.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

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

Hint 1

Find two numbers whose product is $6 \times (- 5) = - 30$ and whose sum is 13.

Hint 2

After factorising, set each factor equal to 0.

Hint 3

Compare the sum of the zeroes with $- b / a$ and their product with $c / a$ .

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: $6 x^{2} + 13 x - 5 = 6 x^{2} + 15 x - 2 x - 5 = 3 x (2 x + 5) - 1 (2 x + 5) = (3 x - 1) (2 x + 5)$ . So the zeroes are $x = \frac{1}{3}$ and $x = - \frac{5}{2}$ .
1 mark
Sum of zeroes $= \frac{1}{3} - \frac{5}{2} = \frac{2 - 15}{6} = - \frac{13}{6}$ , and $- \frac{coefficient of x}{coefficient of x ^{2}} = - \frac{13}{6}$ . Verified.
1 mark
Product of zeroes $= \frac{1}{3} \times (- \frac{5}{2}) = - \frac{5}{6}$ , and $\frac{constant term}{coefficient of x ^{2}} = \frac{- 5}{6}$ . Verified.
1 mark

Answer: Zeroes $\frac{1}{3}$ and $- \frac{5}{2}$ ; sum $= - \frac{13}{6}$ , product $= - \frac{5}{6}$ (relationship verified)

Where the marks are

Factorises and finds the zeroes $\frac{1}{3}, - \frac{5}{2}$ (1 mark)
Verifies the sum of zeroes $= - b / a$ (1 mark)
Verifies the product of zeroes $= c / a$ (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 paper2025 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 26

Hints

Step-by-step solution

Revise the chapter

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