Find the zeroes of the polynomial 4x² + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 29(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section C, question 29(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(a) · 3 marks · Short answerPolynomials

Find the zeroes of the polynomial $4 x^{2} + 4 x -3$ and verify the relationship between zeroes and coefficients of the polynomial.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

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

Hint 1

Find two numbers whose product is $4 \times (- 3) = - 12$ and sum is 4.

Hint 2

After finding the zeroes, compare their sum with $- b / a$ and 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: $4 x^{2} + 4 x - 3 = 4 x^{2} + 6 x - 2 x - 3 = (2 x + 3) (2 x - 1)$
1 mark
Zeroes: $2 x + 3 = 0 \Rightarrow x = - \frac{3}{2}$ ; $2 x - 1 = 0 \Rightarrow x = \frac{1}{2}$ .
1 mark
Sum of zeroes $= - \frac{3}{2} + \frac{1}{2} = - 1$ , and $\frac{- ( coefficient of x )}{coefficient of x ^{2}} = \frac{- 4}{4} = - 1$ . Verified.
½ mark
Product of zeroes $= - \frac{3}{2} \times \frac{1}{2} = - \frac{3}{4}$ , and $\frac{constant term}{coefficient of x ^{2}} = \frac{- 3}{4}$ . Verified.
½ mark

Answer: Zeroes are −3/2 and 1/2; sum = −1 = −b/a, product = −3/4 = c/a

Where the marks are

Factorises as (2x + 3)(2x − 1) (1 mark)
Zeroes −3/2 and 1/2 (1 mark)
Verifies sum of zeroes = −b/a (½ mark)
Verifies product of zeroes = c/a (½ 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 paper2024 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 29(a)

Hints

Step-by-step solution

Revise the chapter

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