Find the zeroes of the quadratic polynomial 5x² + 3x – 2 and verify the relationship between the zeroes and the co-efficients.

Zeroes are 25 and -1; sum = -35, product = -25 (relationships verified)

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

CBSE Class 10 Mathematics Basic 2024: question 29

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerPolynomials

Find the zeroes of the quadratic polynomial $5 x^{2} + 3 x -2$ and verify the relationship between the zeroes and the co-efficients.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Find two numbers whose product is $5 \times (- 2) = - 10$ and sum is 3.

Hint 2

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

Splitting the middle term: $5 x^{2} + 3 x - 2 = 5 x^{2} + 5 x - 2 x - 2 = 5 x (x + 1) - 2 (x + 1) = (5 x - 2) (x + 1)$
1 mark
Zeroes: $5 x - 2 = 0 \Rightarrow x = \frac{2}{5}$ ; $x + 1 = 0 \Rightarrow x = - 1$
1 mark
Sum of zeroes $= \frac{2}{5} + (- 1) = - \frac{3}{5}$ , and $- \frac{coefficient of x}{coefficient of x ^{2}} = - \frac{3}{5}$ . Verified.
½ mark
Product of zeroes $= \frac{2}{5} \times (- 1) = - \frac{2}{5}$ , and $\frac{constant term}{coefficient of x ^{2}} = - \frac{2}{5}$ . Verified.
½ mark

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

Where the marks are

Factorises correctly (1 mark)
Finds zeroes $\frac{2}{5}$ and $- 1$ (1 mark)
Verifies sum $= - b / a$ (½ mark)
Verifies product $= c / a$ (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 430/3/1 (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 29

Hints

Step-by-step solution

Revise the chapter

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