Home

CBSE Class 10 · Boards 2027 · NCERT 2026-27 syllabus

NCERT Exemplar Solutions Class 10 Maths Chapter 2 Polynomials

Try each question first: pick an option or type your final answer, then see the full step-by-step solution. Stuck? Open the first step as a hint. Free, no account needed.

  • Boards begin February 2027
  • Pre-boards are in December
  • Polynomials is in Algebra, which carries 20 of the 80 marks in the 2026-27 CBSE Maths paper

9 NCERT Exemplar questions from Chapter 2

Exercise 2.1

Exemplar Ex 2.1 Q11 mark
If one of the zeroes of the quadratic polynomial (k – 1)x² + kx + 1 is −3, then the value of k is
Exemplar Ex 2.1 Q31 mark
If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and −3, then
Exemplar Ex 2.1 Q41 mark
The number of polynomials having zeroes as −2 and 5 is
Exemplar Ex 2.1 Q71 mark
The zeroes of the quadratic polynomial x² + 99x + 127 are
Exemplar Ex 2.1 Q101 mark
If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it

Exercise 2.2

Exemplar Ex 2.2 Q1(v)2 marks
Can the quadratic polynomial x² + kx + k have equal zeroes for some odd integer k > 1? Justify.

Exercise 2.3

Exemplar Ex 2.3 Q13 marks
Find the zeroes of 4x² – 3x – 1 by factorisation and verify the relationship between zeroes and coefficients.
Exemplar Ex 2.3 Q23 marks
Find the zeroes of 3x² + 4x – 4 by factorisation and verify the relationship between zeroes and coefficients.
Exemplar Ex 2.3 Q83 marks
Find the zeroes of v² + 4√3·v – 15 and verify the relationship between zeroes and coefficients.

CBSE board pattern: Assertion-Reason and case-based questions

Written in the CBSE board format. These are not numbered NCERT/Exemplar questions; some case studies are built on textbook problems. Neither NCERT book has Assertion-Reason questions: they, and case-based questions, are a CBSE board-paper format, here on this chapter's 2026-27 syllabus, with solutions by LazyTopper.

CBSE board pattern · Assertion-Reason1 mark
Assertion (A): If both zeroes of a quadratic polynomial ax² + bx + c are negative, then a, b and c all have the same sign. Reason (R): For ax² + bx + c with zeroes α, β: α + β = −b/a and αβ = c/a.
CBSE board pattern · Assertion-Reason1 mark
Assertion (A): If the zeroes of ax² + bx + c (with c ≠ 0) are equal, then c and a have the same sign. Reason (R): For real, equal zeroes the discriminant b² − 4ac = 0 and the common root is −b/(2a), whose square equals c/a.
CBSE board pattern · Case-based4 marks
A bridge’s arch is modelled by p(x) = x² + (k + 1)x + b. Surveyors find that the arch lands on the x-axis at x = 2 and x = −3. (i) Find b using the product of zeroes. (ii) Find k using the sum of zeroes. (iii) Write the polynomial explicitly. (iv) Verify that x = 2 is indeed a zero of your polynomial.

Would your working get full marks?

Board examiners mark every step. Photograph your written answer and see the marks for each step, and exactly where they were lost. Your first answer check is free.

Check my answer

Questions from the NCERT Class 10 Mathematics Exemplar Problems (the CBSE board-pattern section is in the board format, not numbered book questions); the solutions are written by LazyTopper. LazyTopper is an independent platform and is not affiliated with CBSE or NCERT.

© 2026 P&CGOLDDUST_TECH PRIVATE LIMITEDChaptersCBSE 2027How CBSE marks answersFor parentsPrivacyTermsCancellation & RefundsContactYouTubeInstagramFacebookWhatsApp: ask a doubt