If α, β are zeroes of the polynomial p(x) = 5x² - 7x - 3, then form a quadratic polynomial whose zeroes are (2)/(α) and (2)/(β).

x² + 14/3x - 20/3, i.e. k(3x² + 14x - 20)

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 30(a)

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section C, question 30(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(a) · 3 marks · Short answerPolynomials

If $α, β$ are zeroes of the polynomial $p (x) = 5 x^{2} - 7 x - 3$ , then form a quadratic polynomial whose zeroes are $\frac{2}{α}$ and $\frac{2}{β}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

First find $α + β$ and $α β$ from the coefficients.

Hint 2

Express $\frac{2}{α} + \frac{2}{β}$ and $\frac{2}{α} \cdot \frac{2}{β}$ in terms of $α + β$ and $α β$ , then use $x^{2} - (sum) x + product$ .

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 $5 x^{2} - 7 x - 3$ : $α + β = - \frac{- 7}{5} = \frac{7}{5}$ , $α β = \frac{- 3}{5}$
1 mark
Sum of new zeroes $= \frac{2}{α} + \frac{2}{β} = \frac{2 ( α + β )}{α β} = \frac{2 \times \frac{7}{5}}{- \frac{3}{5}} = - \frac{14}{3}$
½ mark
Product of new zeroes $= \frac{4}{α β} = \frac{4}{- \frac{3}{5}} = - \frac{20}{3}$
½ mark
Required polynomial $= x^{2} - (sum) x + product = x^{2} + \frac{14}{3} x - \frac{20}{3}$ , or $k (3 x^{2} + 14 x - 20)$ , $k \neq = 0$ .
1 mark

Answer: $x^{2} + \frac{14}{3} x - \frac{20}{3}$ , i.e. $k (3 x^{2} + 14 x - 20)$

Where the marks are

$α + β = \frac{7}{5}$ and $α β = - \frac{3}{5}$ (½ + ½ mark)
Sum of new zeroes $- \frac{14}{3}$ (½ mark)
Product of new zeroes $- \frac{20}{3}$ (½ mark)
Writes the polynomial (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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 30(a)

Hints

Step-by-step solution

Revise the chapter

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