If α, β are zeroes of the quadratic polynomial x² + 3x + 2, find a quadratic polynomial whose zeroes are α + 1, β + 1.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 29

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, 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

If $α, β$ are zeroes of the quadratic polynomial $x^{2} + 3 x + 2$ , find a quadratic polynomial whose zeroes are $α + 1$ , $β + 1$ .

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

Hints

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

Hint 1

Find the sum and product of zeroes from the coefficients.

Hint 2

A quadratic with given zeroes is $x^{2} - (sum) x + (product)$ ; expand $(α + 1) (β + 1)$ .

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.

For $x^{2} + 3 x + 2$ : $α + β = - \frac{b}{a} = - 3$ , $α β = \frac{c}{a} = 2$ .
1 mark
Sum of new zeroes: $(α + 1) + (β + 1) = (α + β) + 2 = - 3 + 2 = - 1$ .
½ mark
Product: $(α + 1) (β + 1) = α β + (α + β) + 1 = 2 - 3 + 1 = 0$ .
1 mark
Required polynomial $= x^{2} - (sum) x + product = x^{2} + x$ (or $k (x^{2} + x)$ , $k \neq = 0$ ).
½ mark

Answer: $x^{2} + x$ (or $k (x^{2} + x)$ )

Where the marks are

Finds $α + β = - 3$ and $α β = 2$ (½ + ½ mark)
Sum of new zeroes $= - 1$ (½ mark)
Product of new zeroes $= 0$ (1 mark)
Writes polynomial $x^{2} + x$ (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 paper2023 board paper, set 430/1/1 (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 29

Hints

Step-by-step solution

Revise the chapter

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