If α, β are the zeroes of the polynomial p(x) = 4x² - 3x - 7, then ((1)/(α) + (1)/(β) ) is equal to: (A) 7/3 (B) (-7)/(3) (C) 3/7 (D) (-3)/(7)

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 17

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section A, question 17, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q17 · 1 mark · MCQPolynomials

If $α, β$ are the zeroes of the polynomial $p (x) = 4 x^{2} - 3 x - 7$ , then $(\frac{1}{α} + \frac{1}{β})$ is equal to:

(A) $\frac{7}{3}$
(B) $\frac{- 7}{3}$
(C) $\frac{3}{7}$
(D) $\frac{- 3}{7}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

Combine the fractions: $\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β}$ .

Hint 2

Use sum $= - b / a$ and product $= c / a$ .

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 $4 x^{2} - 3 x - 7$ : $α + β = - \frac{b}{a} = \frac{3}{4}$ and $α β = \frac{c}{a} = - \frac{7}{4}$ .
$\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{3/4}{- 7/4} = - \frac{3}{7}$ . So the answer is option (D).
1 mark

Answer: $- \frac{3}{7}$ , option (D)

Where the marks are

Chooses option (D) $- \frac{3}{7}$ (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 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 17

Hints

Step-by-step solution

Revise the chapter

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