If α, β are the zeroes of a polynomial p(x) = x² + x - 1, then (1)/(α) + (1)/(β) equals to (A) 1 (B) 2 (C) -1 (D) (-1)/(2)

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 7

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q7 · 1 mark · MCQPolynomials

If $α, β$ are the zeroes of a polynomial $p (x) = x^{2} + x - 1$ , then $\frac{1}{α} + \frac{1}{β}$ equals to

(A)1
(B)2
(C)-1
(D) $\frac{- 1}{2}$

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

Hints

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

Hint 1

Combine the two fractions into one.

Hint 2

Use $α + β = - b / a$ and $α β = c / a$ .

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.

For $x^{2} + x - 1$ , the sum of zeroes is $α + β = - \frac{b}{a} = - 1$ and the product is $α β = \frac{c}{a} = - 1$ .
$\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{- 1}{- 1} = 1$ . Option (A).
1 mark

Answer: 1, option (A)

Where the marks are

Uses the sum and product of zeroes to get 1, option (A) (1 mark)

Revise the chapter

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

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 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 7

Hints

Step-by-step solution

Revise the chapter

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