CBSE Class 10 Maths Chapter 17 Polynomials NCERT Solutions
CBSE Class 10 Mathematics Chapter 17, Polynomials, introduces students to the graphical interpretation of polynomial zeroes. This chapter explores how the number of times a polynomial's graph intersects the x-axis directly indicates the number of its zeroes. The NCERT Solutions provide detailed, step-by-step explanations for various problems, enabling students to confidently determine the number of zeroes from given graphs. Mastering this concept is essential for a solid understanding of algebraic principles and is a key area for exam preparation. These solutions aim to clarify the relationship between graphical representations and the algebraic properties of polynomials, fostering a deeper comprehension of the subject matter.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 17 |
Chapter summary
Chapter 17 on Polynomials for Class 10 Maths NCERT Solutions focuses on identifying the number of zeroes of a polynomial by examining its graphical representation. The solutions explain the fundamental concept that the number of zeroes is equal to the number of points where the graph of y = p(x) intersects the x-axis. This chapter is essential for visualizing algebraic concepts and reinforcing understanding of polynomial properties.
Learning outcomes
- Understand the relationship between the graph of a polynomial and its zeroes.
- Determine the number of zeroes of a polynomial from its given graph.
- Visualize the concept of zeroes of a polynomial graphically.
- Apply graphical interpretation to solve problems related to polynomials.
Topics covered
Paper topics
- Polynomials
- Zeroes of a polynomial
- Graphical representation of polynomials
- Number of zeroes from graph
- Intersection with x-axis
- Linear graphs
- Quadratic graphs
- Cubic graphs
Important topics
- Number of zeroes from graph
- Graphical interpretation of zeroes
- Relationship between graph and zeroes
PDF preview
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Questions and Solutions
Exercise 2.1
Question 1
The graphs of are given in the following figures for some polynomials . Find the number of zeroes of , in each case.
Solution: The number of zeroes of a polynomial is equal to the number of points where the graph of intersects the x-axis. We will examine each graph provided.
(i) The given graph intersects the x-axis at one point. Therefore, the number of zeroes is 1.
(ii) The given graph intersects the x-axis at two points. Therefore, the number of zeroes is 2.
(iii) The given graph intersects the x-axis at three points. Therefore, the number of zeroes is 3.
(iv) The given graph intersects the x-axis at one point. Therefore, the number of zeroes is 1.
(v) The given graph intersects the x-axis at four points. Therefore, the number of zeroes is 4.
(vi) The given graph intersects the x-axis at three points. Therefore, the number of zeroes is 3.
Common mistakes
- Confusing intersection with the y-axis for zeroes (which are on the x-axis).
- Miscounting the number of intersection points.
- Assuming a graph represents a polynomial when it doesn't intersect the x-axis at all.
Revision tips
- Focus on the definition of zeroes: points where the graph crosses the x-axis.
- Practice identifying intersection points carefully for each graph.
- Review the relationship between the degree of a polynomial and the maximum number of zeroes it can have.
Practice MCQs
Q1. What does the number of zeroes of a polynomial p(x) represent graphically?
Explanation: The number of zeroes of a polynomial p(x) is determined by the number of points where its graph, y = p(x), intersects the x-axis.
Q2. If a graph of y = p(x) does not intersect the x-axis at any point, how many zeroes does the polynomial p(x) have?
Explanation: If the graph of y = p(x) does not intersect the x-axis, it means there are no real values of x for which p(x) = 0, hence the polynomial has no real zeroes.
Q3. For a polynomial p(x), if its graph intersects the x-axis at exactly two distinct points, what can be said about the number of its zeroes?
Explanation: Each point of intersection with the x-axis corresponds to a real zero of the polynomial. Two intersection points mean two real zeroes.
Frequently asked questions
What is the main concept covered in Chapter 17 of Class 10 Maths NCERT Solutions?
Chapter 17 focuses on understanding the number of zeroes of a polynomial by examining its graphical representation. It explains that the number of zeroes is equal to the number of points where the graph intersects the x-axis.
How can I find the number of zeroes of a polynomial from its graph?
To find the number of zeroes, count the number of points where the graph of the polynomial y = p(x) crosses or touches the x-axis. Each such point represents a zero.
What does it mean if a polynomial's graph does not intersect the x-axis?
If a polynomial's graph does not intersect the x-axis, it means that the polynomial has no real zeroes.
Are these solutions suitable for exam revision?
Yes, these solutions provide clear explanations and graphical interpretations, which are essential for revising the concepts of zeroes of polynomials and how they relate to their graphs for exams.
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