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

Zeroes 32 and -13; sum 76 and product -12 verified.

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 27

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerPolynomials

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 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 $6 \times (- 3) = - 18$ 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.

$6 x^{2} - 7 x - 3 = 6 x^{2} - 9 x + 2 x - 3 = 3 x (2 x - 3) + 1 (2 x - 3) = (2 x - 3) (3 x + 1)$
1 mark
Zeroes: $2 x - 3 = 0 \Rightarrow x = \frac{3}{2}$ ; $3 x + 1 = 0 \Rightarrow x = - \frac{1}{3}$
1 mark
Sum of zeroes $= \frac{3}{2} - \frac{1}{3} = \frac{7}{6}$ and $- \frac{coeff. of x}{coeff. of x ^{2}} = - \frac{- 7}{6} = \frac{7}{6}$ . Verified.
½ mark
Product of zeroes $= \frac{3}{2} \times (- \frac{1}{3}) = - \frac{1}{2}$ and $\frac{constant term}{coeff. of x ^{2}} = \frac{- 3}{6} = - \frac{1}{2}$ . Verified.
½ mark

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

Where the marks are

Factorises as $(2 x - 3) (3 x + 1)$ (1 mark)
Finds zeroes $\frac{3}{2}, - \frac{1}{3}$ (1 mark)
Verifies sum of zeroes (½ mark)
Verifies product of zeroes (½ 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 paper2024 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 2024: question 27

Hints

Step-by-step solution

Revise the chapter

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