If α and β are roots of the quadratic equation x² - 7x + 10 = 0, find the quadratic equation whose roots are α² and β².

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 29(B)

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section C, question 29(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(B) · 3 marks · Short answerQuadratic Equations

If $α$ and $β$ are roots of the quadratic equation $x^{2} - 7 x + 10 = 0$ , find the quadratic equation whose roots are $α^{2}$ and $β^{2}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

Write the sum and the product of the roots from the coefficients.

Hint 2

Express $α^{2} + β^{2}$ using $(α + β)^{2}$ , then use $x^{2} - S x + P = 0$ .

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 $x^{2} - 7 x + 10 = 0$ : $α + β = 7$ and $α β = 10$ .
½ mark
Sum of new roots: $α^{2} + β^{2} = (α + β)^{2} - 2 α β = 49 - 20 = 29$ .
1 mark
Product of new roots: $α^{2} β^{2} = (α β)^{2} = 100$ .
1 mark
The required equation is $x^{2} - (sum) x + product = 0$ , i.e. $x^{2} - 29 x + 100 = 0$ .
½ mark

Answer: $x^{2} - 29 x + 100 = 0$

Where the marks are

Writes $α + β = 7$ and $α β = 10$ (½ mark)
Finds $α^{2} + β^{2} = 29$ (1 mark)
Finds $α^{2} β^{2} = 100$ (1 mark)
Forms $x^{2} - 29 x + 100 = 0$ (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 30/6/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 29(B)

Hints

Step-by-step solution

Revise the chapter

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