If α and β are the zeroes of the quadratic polynomial 2x² - 8x + 5, then find the value of (α + (1)/(β) ) × (β + (1)/(α) ).

MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 27

From the official CBSE sample question paper for 2026-27, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerPolynomials

If $α$ and $β$ are the zeroes of the quadratic polynomial $2 x^{2} - 8 x + 5$ , then find the value of $(α + \frac{1}{β}) \times (β + \frac{1}{α})$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Write down the sum and product of zeroes from the coefficients of the polynomial.

Hint 2

Combine $α + \frac{1}{β}$ into a single fraction, and do the same for the other bracket. The whole expression then depends only on $α β$ .

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 $2 x^{2} - 8 x + 5$ : $α + β = - \frac{- 8}{2} = 4$ and $α β = \frac{5}{2}$ .
1 mark
Combine each bracket into one fraction:
$(α + \frac{1}{β}) (β + \frac{1}{α}) = \frac{α β + 1}{β} \times \frac{α β + 1}{α} = \frac{( α β + 1 ) ^{2}}{α β}$ .
½ mark
Substitute $α β = \frac{5}{2}$ : $\frac{( \frac{5}{2} + 1 ) ^{2}}{\frac{5}{2}} = \frac{\frac{49}{4}}{\frac{5}{2}}$ .
1 mark
$= \frac{49}{4} \times \frac{2}{5} = \frac{49}{10}$ .
½ mark

Answer: $\frac{49}{10}$

Where the marks are

Finds sum of zeroes = 4 and product = $\frac{5}{2}$ (1 mark)
Rewrites the expression as $\frac{( α β + 1 ) ^{2}}{α β}$ (½ mark)
Substitutes the value of $α β$ (1 mark)
Simplifies to $\frac{49}{10}$ (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 paperSample paper 2026-27 (Standard): 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 Standard sample paper 2026-27: question 27

Hints

Step-by-step solution

Revise the chapter

More questions from Polynomials