MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 22(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerPolynomials

Find a quadratic polynomial whose zeroes are 6 and $- 3$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

A quadratic with zeroes α and β can be written as $x^{2} - (α + β) x + α β$ .

Hint 2

Compute α+β and αβ for 6 and −3.

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.

Sum of zeroes $= 6 + (- 3) = 3$
½ mark
Product of zeroes $= 6 \times (- 3) = - 18$
½ mark
Required polynomial $= x^{2} - (sum) x + (product) = x^{2} - 3 x - 18$ , or more generally $k (x^{2} - 3 x - 18)$ , $k \neq = 0$ .
1 mark

Answer: $x^{2} - 3 x - 18$ (or $k (x^{2} - 3 x - 18)$ )

Where the marks are

Finds sum of zeroes = 3 (½ mark)
Finds product of zeroes = −18 (½ mark)
Writes polynomial $x^{2} - 3 x - 18$ (1 mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Forming a Quadratic Polynomial from Its Zeros

Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 430/6/1 (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 2023: question 22(a)

Hints

Step-by-step solution

Revise the chapter

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