If p and q are zeroes of the polynomial p(y) = 21y² - y - 2, then find the value of (1 - p) · (1 - q).

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 21

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerPolynomials

If p and q are zeroes of the polynomial $p (y) = 21 y^{2} - y - 2$ , then find the value of $(1 - p) \cdot (1 - q)$ .

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

Expand $(1 - p) (1 - q)$ first.

Hint 2

The expansion uses only $p + q$ and $pq$ . Get these from the coefficients: $- \frac{b}{a}$ and $\frac{c}{a}$ .

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.

Here $a = 21$ , $b = - 1$ , $c = - 2$ . Sum of zeroes: $p + q = - \frac{b}{a} = \frac{1}{21}$ .
½ mark
Product of zeroes: $pq = \frac{c}{a} = - \frac{2}{21}$ .
½ mark
$(1 - p) (1 - q) = 1 - (p + q) + pq = 1 - \frac{1}{21} - \frac{2}{21}$ .
½ mark
$= \frac{21 - 1 - 2}{21} = \frac{18}{21} = \frac{6}{7}$ .
½ mark

Answer: $(1 - p) (1 - q) = \frac{6}{7}$

Where the marks are

Writes $p + q = \frac{1}{21}$ (½ mark)
Writes $pq = - \frac{2}{21}$ (½ mark)
Expands to $1 - (p + q) + pq$ and substitutes (½ mark)
Gets $\frac{18}{21} = \frac{6}{7}$ (½ mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Relationship Between Zeros and Coefficients

Practise this chapterBoard-style questions from Polynomials, 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 21

Hints

Step-by-step solution

Revise the chapter

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