Home · Schooling · CBSE · Class 10 · Mathematics · Polynomials · Exercise 2.1
NCERT Class 10 Mathematics Exercise 2.1 Solutions: Polynomials
AI-written, checked on 23 Oct 2026
Solutions written by Shishya, checked — not the board's official answers
Step-by-step working for every question of Exercise 2.1 in NCERT's Class 10 Mathematics book, chapter “Polynomials”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.
How these were checked: the solutions were drafted with AI and then read and corrected on 23 Oct 2026. Every numerical final answer is recomputed from the question's own numbers by a calculator check that runs before each release; proofs and explanations were read, not machine-checked. The NCERT textbook is the authority — if something here disagrees with it, follow the book.
Tap “why?” under a step to see the textbook rule it uses — from Shishya's fixed list of NCERT Class 9-10 rules, not written by AI for this page. A step without one has no rule from the list yet.
Stuck on a step?
Ask the AI tutor about this chapter — it gives hints before answers — or snap a photo of your own question to get worked steps. You will be talking to an AI, not a person. For ages 13 and up; the first answer of each is free.
Ex 2.1 Q1
Six graphs of y = p(x) are drawn in the book (Fig. 2.10, parts (i) to (vi)). Find the number of zeroes of p(x) in each case.
Uses a figure printed in the NCERT book — open the chapter above to see it.
- The zeroes of p(x) are the x-coordinates of the points where the graph of y = p(x) meets the x-axis, so count those points in each graph.
- (i) The graph is a line parallel to the x-axis and never meets it: no zero.
- (ii) The graph cuts the x-axis at exactly one point: one zero.
- (iii) The graph meets the x-axis at three points: three zeroes.
- (iv) The graph meets the x-axis at two points: two zeroes.
- (v) The graph meets the x-axis at four points: four zeroes.
- (vi) The graph meets the x-axis at three points (touching it at one of them): three zeroes.
Answer: (i) 0; (ii) 1; (iii) 3; (iv) 2; (v) 4; (vi) 3
Other exercises in this chapter
- Exercise 2.2 — 2 questions
← Polynomials: notes, practice and all exercises
Saves these solutions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.