Find the roots of the quadratic equation x² - x - 2 = 0.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 23(B)

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section B, question 23(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(B) · 2 marks · Very short answerQuadratic Equations

Find the roots of the quadratic equation $x^{2} - x - 2 = 0$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Find two numbers whose product is −2 and sum is −1.

Hint 2

Those numbers are −2 and +1; split the middle term.

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: $x^{2} - 2 x + x - 2 = 0 \Rightarrow x (x - 2) + 1 (x - 2) = 0 \Rightarrow (x - 2) (x + 1) = 0$
1 mark
$x - 2 = 0 \Rightarrow x = 2$ ; $x + 1 = 0 \Rightarrow x = - 1$
1 mark

Answer: x = 2, x = −1

Where the marks are

Factorises as $(x - 2) (x + 1) = 0$ (1 mark)
Each root 2 and −1 (½ + ½ mark)

Revise the chapter

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

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 430/4/1 (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 23(B)

Hints

Step-by-step solution

Revise the chapter

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