The quadratic equation whose roots are 7 and 1/7 is : (A) 7x² - 50x + 7 = 0 (B) 7x² - 50x + 1 = 0 (C) 7x² + 50x - 7 = 0 (D) 7x² + 50x - 1 = 0

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 3

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQQuadratic Equations

The quadratic equation whose roots are $7$ and $\frac{1}{7}$ is :

(A) $7 x^{2} - 50 x + 7 = 0$
(B) $7 x^{2} - 50 x + 1 = 0$
(C) $7 x^{2} + 50 x - 7 = 0$
(D) $7 x^{2} + 50 x - 1 = 0$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

A quadratic with given roots is $x^{2} - (sum of roots) x + (product of roots) = 0$ .

Hint 2

Find the sum and the product of $7$ and $\frac{1}{7}$ , then clear the fraction.

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.

Sum of roots $= 7 + \frac{1}{7} = \frac{50}{7}$ . Product of roots $= 7 \times \frac{1}{7} = 1$ .
½ mark
The equation is $x^{2} - \frac{50}{7} x + 1 = 0$ . Multiplying by 7 gives $7 x^{2} - 50 x + 7 = 0$ . Option (A).
½ mark

Answer: $7 x^{2} - 50 x + 7 = 0$ , option (A)

Where the marks are

Uses $x^{2} - (sum) x + product = 0$ to reach option (A) (1 mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 3

Hints

Step-by-step solution

Revise the chapter

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