The value of p for which roots of the quadratic equation x² - px + 6 = 0 are rational, is (A) 1 (B) -5 (C) 25 (D) √(5)

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 9

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQQuadratic Equations

The value of $p$ for which roots of the quadratic equation $x^{2} - p x + 6 = 0$ are rational, is

(A) $1$
(B) $- 5$
(C) $25$
(D) $5$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Rational roots need the discriminant to be a perfect square.

Hint 2

Compute $p^{2} - 24$ for each option.

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.

Roots are rational when $D = p^{2} - 24$ is a perfect square.
$p = - 5$ : $D = 25 - 24 = 1 = 1^{2}$ (roots 2... actually $- 2, - 3$ ). Others: $p = 1$ gives $- 23$ , $p = 25$ gives $601$ , $p = 5$ gives $- 19$ . Option (B).
1 mark

Answer: $p = - 5$ , option (B)

Where the marks are

Checks $p^{2} - 24$ is a perfect square for $p = - 5$ (1 mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Nature of Roots and Discriminant

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 9

Hints

Step-by-step solution

Revise the chapter

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