If f(x) = px² + qx + r, p ≠ 0 and p + r = q, then one of the zeroes of f(x) is: (A) q/p (B) r/p (C) -r/p (D) -q/p

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

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 2

From the official CBSE sample question paper for 2026-27, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQPolynomials

If $f (x) = p x^{2} + q x + r$ , $p \neq = 0$ and $p + r = q$ , then one of the zeroes of $f (x)$ is:

(A) $\frac{q}{p}$
(B) $\frac{r}{p}$
(C) $- \frac{r}{p}$
(D) $- \frac{q}{p}$

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

Replace q by p + r.

Hint 2

Group the terms to take out the factor (x + 1).

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 $q = p + r$ into the polynomial: $f (x) = p x^{2} + (p + r) x + r$ .
Factorise: $p x^{2} + p x + r x + r = p x (x + 1) + r (x + 1) = (x + 1) (p x + r)$ .
1 mark
The zeroes are $- 1$ and $- \frac{r}{p}$ , so the answer is option (C).

Answer: $- \frac{r}{p}$ , option (C)

Where the marks are

Substitutes q = p + r and factorises to get the zero $- \frac{r}{p}$ (1 mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Forming a Quadratic Polynomial from Its Zeros

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 2

Hints

Step-by-step solution

Revise the chapter

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