If α, β are the zeroes of polynomial p(x) = 6x² – 5x – 3, then find the value of (1)/(α) + (1)/(β).

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 22(a)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerPolynomials

If $α, β$ are the zeroes of polynomial $p (x) = 6 x^{2} -5 x -3$ , then find the value of $\frac{1}{α} + \frac{1}{β}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Recall the relations between the zeroes and the coefficients of a quadratic polynomial.

Hint 2

Combine $\frac{1}{α} + \frac{1}{β}$ into a single fraction.

Hint 3

The result is (sum of zeroes) ÷ (product of zeroes).

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 $6 x^{2} - 5 x - 3$ : $a = 6, b = - 5, c = - 3$ . So $α + β = - \frac{b}{a} = \frac{5}{6}$ and $α β = \frac{c}{a} = \frac{- 3}{6} = - \frac{1}{2}$ .
1 mark
$\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{5/6}{- 1/2} = - \frac{5}{3}$
1 mark

Answer: $\frac{1}{α} + \frac{1}{β} = - \frac{5}{3}$

Where the marks are

Writes sum $= \frac{5}{6}$ and product $= - \frac{3}{6}$ of zeroes (1 mark)
Uses $\frac{α + β}{α β}$ to get $- \frac{5}{3}$ (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 paper2026 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 22(a)

Hints

Step-by-step solution

Revise the chapter

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