If (1 - p) is a root of the quadratic equation x² + px + 1 - p = 0, then its roots are: (A) 0, 1 (B) -1, 1 (C) 0, -1 (D) -1, 2

MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 4

From the official CBSE sample question paper for 2026-27, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQQuadratic Equations

If $(1 - p)$ is a root of the quadratic equation $x^{2} + p x + 1 - p = 0$ , then its roots are:

(A) $0, 1$
(B) $- 1, 1$
(C) $0, - 1$
(D) $- 1, 2$

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

A root satisfies the equation, so substitute x = 1 − p.

Hint 2

Take (1 − p) common to find p.

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.

Put $x = 1 - p$ : $(1 - p)^{2} + p (1 - p) + (1 - p) = 0 \Rightarrow (1 - p) (1 - p + p + 1) = 0 \Rightarrow 2 (1 - p) = 0 \Rightarrow p = 1$ .
1 mark
The equation becomes $x^{2} + x = 0$ , so $x (x + 1) = 0$ and the roots are $0$ and $- 1$ . This is option (C).

Answer: 0, −1, option (C)

Where the marks are

Finds p = 1 and solves x² + x = 0 to get roots 0, −1 (1 mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Standard Form of a Quadratic Equation

Practise this chapterBoard-style questions from Quadratic Equations, 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.

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CBSE Class 10 Mathematics Standard sample paper 2026-27: question 4

Hints

Step-by-step solution

Revise the chapter

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