α, β are zeroes of the polynomial 2x² + 5x + 1. The value of ((1)/(α) + (1)/(β) ) is: (A) -5/4 (B) 5 (C) 5/4 (D) -5

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 9

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQPolynomials

$α$ , $β$ are zeroes of the polynomial $2 x^{2} + 5 x + 1$ . The value of $(\frac{1}{α} + \frac{1}{β})$ is:

(A) $- \frac{5}{4}$
(B)5
(C) $\frac{5}{4}$
(D) $- 5$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

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

Hint 1

Combine the two fractions into a single fraction.

Hint 2

You need $α + β$ and $α β$ from the coefficients.

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 $2 x^{2} + 5 x + 1$ : $α + β = - \frac{5}{2}$ and $α β = \frac{1}{2}$ .
½ mark
$\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{- 5/2}{1/2} = - 5$ . Hence option (D).
½ mark

Answer: −5, option (D)

Where the marks are

Writes the sum and product of the zeroes (½ mark)
Gets $\frac{1}{α} + \frac{1}{β} = - 5$ (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 paper2025 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 2025: question 9

Hints

Step-by-step solution

Revise the chapter

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