NCERT Solutions for Class 9 Political Science Chapter 2

August 8, 202239 Insightful Publications

**NCERT Solutions Class 10 Maths Chapter 2: **To help students study effectively for their exams, NCERT solutions for Class 10 Maths chapter 2 – Polynomials – are offered here. Subject experts create these solutions at Embibe to help students prepare for their board exams. To make it simpler for students to practice the chapter 2 Polynomials questions using the NCERT solutions, these solutions are solved in a certain method.

Including step-by-step explanations of these Maths NCERT Class 10 solutions make studying easier for the students. These solutions are structured so students can gain information and build a conceptual foundation before moving on to more challenging topics. Students can quickly master the new concepts and solve the exercise problems by using the NCERT solutions provided by Embibe. You can download the Class 10 Maths chapter 2 solutions PDF for free from the Embibe platform and access it offline. Scroll down to know more.

Practice CBSE Class 10 Subject Wise Questions | |
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Practice Questions from CBSE Class 10 Books Mathematics | |

Practice Questions from CBSE Class 10 Books Science | |

Practice Questions from CBSE Class 10 Books Social Science |

The Class 10 Maths chapter 2 NCERT solutions consists of exercise 2.1, exercise 2.2, exercise 2.3, and exercise 2.4. However, before we jump into further details, let us have an overview of the exercises from the table below:

Particulars | Details |
---|---|

Exercise 2.1 | Introduction |

Exercise 2.2 | Geometrical Meaning of the Zeroes of a Polynomial |

Exercise 2.3 | Relationship between Zeroes and Coefficients of a Polynomial |

Exercise 2.4 | Division Algorithm for Polynomials |

The solutions for Class 10 Maths chapter 2 provided in this article include the answers to all exercise questions in a simple and understandable manner. Students can refer to the NCERT solutions PDF to solve their assignments. Mastering Polynomials NCERT solutions will help students prepare for their Class 10 board exam.

**Q.1. The graph of y=p(x) is given in the figure below, for some polynomial p(x). Find the number of zeroes of p(x).**

**Solution: **We know that,

If a polynomial px is of degree n, then the graph of y=px intersects the x-axis at most n points.

Therefore, a polynomial px of degree n has at most n zeroes.

Here, the graph of p(x) passes through only y-axis and does not cut the x-axis at all. Therefore, the number of zeroes is 0.

**Q.2. The graph of y=p(x) is given in the figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.**

**Solution:** Given the graph of y=p(x)

We know that the point of intersections of a graph with the X- axis are called roots or zeroes of the given equation or polynomial. Here, as the graph of p(x) intersects the x-axis at only

1 point. Therefore, the number of zeroes is 1.

**Q.3. The graph of y=p(x) is given below for a polynomial p(x). Find the number of zeroes of p(x).**

**Solution: **Given graph is:

We can see that, the graph of y=px is intersecting the x-axis at three points. The number of points of intersection of the graph with the x-axis denotes the number of zeroes of the polynomial.

DOWNLOAD NCERT SOLUTIONS FOR CLASS 10 MATHS CHAPTER 2

The study of Polynomials is the continuation of topics studied in Class 9.** **Polynomial is an expression consisting of variables and coefficients that involves operations of addition, subtraction, multiplication, and non-negative integer exponents.

Polynomials play an essential role in describing the most natural phenomena around us. From Newtonian equations to designing a roller coaster, polynomials are part and parcel of almost everything one can express in mathematical notions.

A polynomial, in particular, has a wide range of applications. To name a few, we have the following:

- The most famous Newtonian equation describing an object’s displacement is an example of a polynomial. The equation is as follows: s = ut + ½at².
- Statisticians use mathematical models based on polynomials to analyse and interpret data and arrive at required conclusions. In financial planning, polynomials are used to calculate the interest rate based on the principal amount and the number of years.
- Polynomials are also used in Meteorology. Polynomials are useful, from mapping weather patterns to tracing the paths of celestial objects.
- Many engineering careers also use polynomials. Aerospace, Mechanical and Electrical engineers are required to use polynomials for designing in their respective fields. Aerospace may require the designing of rockets, while the mechanical field needs the designing of various motors. Voltage drops in electrical and electronics are also expressed as polynomials.
- Polynomials are also used in medical fields to monitor the status of the patients, their intake, and body conditions.
- Designing a roller coaster and its trajectory also use polynomials.

Some of the advantages of solving the **NCERT Solutions** by Embibe are given below:

- These NCERT solutions are prepared in an elaborate manner so that the students can easily understand the topics.
- With the help of NCERT solutions on polynomials, students can quickly learn about the zeroes and coefficients of a polynomial and the division algorithm for polynomials.
- Our academic experts have prepared all NCERT solutions according to the latest revised CBSE Syllabus and NCERT guidelines.
- Students can use these NCERT solutions for revision before exams or tests.
- The NCERT solutions by Embibe will not only help you in preparing for board exams but also for competitive exams and Olympiads as well.
- Embibe’s NCERT solutions for all the subjects can be accessed and downloaded for free.

The solved examples from the Polynomials chapter are mentioned below:

**Q.1. For the given cubic polynomial x ^{3} + ax^{2} + bx + c, one of the zeroes is –1. Find the product of the other two zeroes.**The product of the other two zeroes is (b – a + 1).

Ans.

**Q.2. Find the values of ‘a’ and ‘b’ of the given quadratic polynomial x ^{2} + (a + 1)x + b. The zeroes of the polynomial are 2 and –3.Ans. **The value of ‘a’ is 0, and ‘b’ is -6.

**Q.3. You are given a polynomial x ^{3} + 4x^{2} – px + 8, which is divisible by (x – 2). Determine the value of ‘p’ in the polynomial.**The value of ‘p’ is 16.

Ans.

**Q.4. Find the degree of the given polynomial: (x + 1)(x ^{2} – x – x^{4} +1)**The degree of the given polynomial is 5.

Ans.

**Q.5. Find the value of ‘k’ for a quadratic polynomial (k – 1)x ^{2}+kx +1. One of the zeroes of the polynomial is given as –3.Ans. **The value of ‘k’ is 4/3.

**Q.6. Why should students prepare from CBSE Class 10 Maths Chapter 2 NCERT solutions by Embibe for my CBSE exams?Ans.** The NCERT Solutions provided by Embibe are prepared by experts to help students to score good marks in their CBSE exams. The students should refer to the NCERT Solutions by Embibe to develop a sound understanding of all the concepts.

**Q.7. Can NCERT Solutions help me to score maximum marks in exams?Ans.** Studying from NCERT Solutions will help students gain a conceptual understanding of all the concepts, which will help students to score good marks in the exams.

**Ans: **Students can find and download the NCERT solutions for Class 10 Maths on Embibe.

**Ans: **The NCERT solutions provided by Embibe are reliable as they are prepared by the subject experts to help students with their studies.

**Ans: **Yes, the NCERT solutions for Class 10 Maths are available in PDF format.

**Ans: **Yes, the NCERT solutions for Class 10 Maths chapter 2 are available for free on Embibe.

**Ans: **Yes, students can access free mock test for Class 10 Maths on Embibe.

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