Exercise 2.1: Number of zeroes from a graph
What it tests. The zeroes of \(p(x)\) are the x-coordinates of the points where the graph of \(y = p(x)\) meets the x-axis. Count the meeting points (touching counts too).
NCERT Solutions for Class 10 Maths Chapter 2: Polynomials
Zeroes of a polynomial read from its graph, and the relationship between the zeroes and coefficients of a quadratic: \(\alpha + \beta = -\dfrac{b}{a}\), \(\alpha\beta = \dfrac{c}{a}\). Our own step-by-step solutions to Exercises 2.1 and 2.2, one page per exercise, set out for step marks.
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Chapter 2 exercises
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Exercise 2.2: Zeroes and coefficients of a quadratic
What it tests. For \(ax^2 + bx + c\) with zeroes \(\alpha, \beta\): \(\alpha + \beta = -\dfrac{b}{a}\) and \(\alpha\beta = \dfrac{c}{a}\). Conversely, \(x^2 - (\alpha + \beta)x + \alpha\beta\) has zeroes \(\alpha, \beta\).
Done the NCERT exercises? The board paper asks more
Polynomials has 39 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Polynomials · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.