NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials Exercise 2.1 are provided here to help students in their Class 10 exam preparations. These solutions have been prepared by our subject experts to ensure that students understand key concepts in polynomials effectively. The solutions are explained in simple, step-by-step language with clear examples, enabling students to solve the problems with confidence.
Exercise 2.1 introduces the basic concepts of polynomials, including degree, coefficients, and types of polynomials. This exercise helps students practice identifying polynomials, their degree, and classifying them. By practicing these problems, students can get a solid understanding of polynomial expressions and prepare for higher-level algebraic problems.
NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials Exercise 2.1
Q.
The graphs of y = p(x) are given in figures below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
Q.
Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:
[CBSE - 2025]
Q.
The graph of y = p(x) is given, for a polynomial p(x). The number of zeroes of p(x) from the graph is
[CBSE - 2023]
NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials Exercise 2.1
The NCERT solutions are aligned with the latest CBSE syllabus and provide clear explanations of each question, helping students solve polynomial-related problems easily and score well in exams.
Q. 1 The graphs of y=p(x) are given in the figures below for some polynomials p(x). Find the number of zeroes of p(x), in each case.
Answer:
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(i) Number of zeroes: 0
The given graph does not intersect the x-axis, meaning there are no zeroes because no point on the graph touches or crosses the x-axis. Hence, the number of zeroes is 0.
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(ii) Number of zeroes: 1
The graph intersects the x-axis at exactly one point, meaning there is only 1 zero of the polynomial.
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(iii) Number of zeroes: 3
The graph intersects the x-axis at three points, which means the polynomial has 3 distinct zeroes.
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(iv) Number of zeroes: 2
The graph intersects the x-axis at two points, indicating that the polynomial has 2 zeroes.
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(v) Number of zeroes: 4
The graph intersects the x-axis at four points, meaning the polynomial has 4 zeroes.
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(vi) Number of zeroes: 3
The graph intersects the x-axis at three points, so the polynomial has 3 zeroes.
Q. 2 Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:
Answer:
Q. 3 The graph of y=p(x) is given for a polynomial p(x). The number of zeroes of p(x) from the graph is:
Answer:
FAQs: Class 10 Maths Chapter 2 – Polynomials Exercise 2.1
Q1. What are polynomials?
Answer:
A polynomial is an algebraic expression made up of terms that are non-negative integer powers of variables. For example, ax² + bx + c is a polynomial in x, where a, b, c are constants.
Q2. How do I identify the degree of a polynomial?
Answer:
The degree of a polynomial is the highest power of the variable in the expression. For example, in 2x³ + 5x² - 3, the degree is 3 because the highest power of x is 3.
Q3. What is the difference between a monomial, binomial, and trinomial?
Answer:
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A monomial has one term (e.g., 5x).
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A binomial has two terms (e.g., x + 2).
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A trinomial has three terms (e.g., x² + 3x + 2).
Q4. How do NCERT Solutions for Exercise 2.1 help with exam preparation?
Answer:
These solutions provide clear, step-by-step explanations for identifying and classifying polynomials, which helps students gain a strong foundation in algebra. Practicing these solutions ensures concept clarity and improves problem-solving skills for the exams.
Q5. Are there any tips for solving problems in Exercise 2.1?
Answer:
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Carefully identify the terms in the polynomial.
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Look for the highest power of the variable to determine the degree.
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Classify polynomials based on their terms (monomial, binomial, trinomial).