α and β are the zeroes of the polynomial 5x² - 16x - 10. Find the value of (α)/(β) + (β)/(α).

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 25

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerPolynomials

$α$ and $β$ are the zeroes of the polynomial $5 x^{2} - 16 x - 10$ . Find the value of $\frac{α}{β} + \frac{β}{α}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Find the sum and product of zeroes using the coefficients.

Hint 2

Combine the fractions: $\frac{α ^{2} + β ^{2}}{α β}$ , and write $α^{2} + β^{2}$ in terms of $α + β$ and $α β$ .

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 $5 x^{2} - 16 x - 10$ : $α + β = - \frac{b}{a} = \frac{16}{5}$ and $α β = \frac{c}{a} = \frac{- 10}{5} = - 2$ .
1 mark
$\frac{α}{β} + \frac{β}{α} = \frac{α ^{2} + β ^{2}}{α β} = \frac{( α + β ) ^{2} - 2 α β}{α β} = \frac{\frac{256}{25} + 4}{- 2}$
½ mark
$= \frac{\frac{356}{25}}{- 2} = - \frac{178}{25}$
½ mark

Answer: $- \frac{178}{25}$

Where the marks are

Writes $α + β = \frac{16}{5}$ and $α β = - 2$ (1 mark)
Uses $\frac{( α + β ) ^{2} - 2 α β}{α β}$ with substitution (½ mark)
Gets $- \frac{178}{25}$ (½ 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 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 25

Hints

Step-by-step solution

Revise the chapter

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