Best and Accurate NCERT Solutions Class 10 Math Chapter 2 Polynomials | Maths class 10 ncert solutions | Maths ncert solutions class 10 | 10th class math textbook and solutions | Chapter 2 class 10 maths Solutions
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NCERT Solutions for Class 10 Maths Unit 2
Polynomials Class 10
Unit 2 Polynomials Exercise 2.1, 2.2, 2.3 2.4, 2.4 Solutions
Exercise 2.1 : Solutions of Questions
Q1 :
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes ofp(x), in each case.
(i)
Answer :
(i) The number of zeroes is 0 as the graph does not cut the x-axis at any point.
(ii) The number of zeroes is 1 as the graph intersects the x-axis at only 1 point.
(iii) The number of zeroes is 3 as the graph intersects the x-axis at 3 points.
(iv) The number of zeroes is 2 as the graph intersects the x-axis at 2 points.
(v) The number of zeroes is 4 as the graph intersects the x-axis at 4 points.
(vi) The number of zeroes is 3 as the graph intersects the x-axis at 3 points.
Exercise 2.2 : Solutions of Questions
Q1 :
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
Answer:
Q2 :
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Let the polynomial be ax2 + bx + c,
and its zeroes be a and
Exercise 2.3 : Solutions of Questions
Q1 :
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
Quotient = - x2 - 2 Remainder = - 5x+10
Q2 :
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
Therefore, the relationship between the zeroes and the coefficients is verified.
Q3 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
Q4 :
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, - 14 respectively.
Answer :
Q. 6
On dividing x3-3x2+x+2 by a polynomial g(x), the quotient and remainder were x - 2 and - 2x + 4, respectively. Find g(x).
Answer :
Q7 :
Give examples of polynomial p(x),
g(x),
q(x)
and r(x), which satisfy the division algorithm and
(i (i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
Answer :
According to the division
algorithm, if p(x) and
g(x) are two polynomials with
g(x) ≠ 0, then we can
find polynomials q(x) and r(x) such
that
p(x) = g(x) × q(x) + r(x),
where r(x) = 0 or degree
of r(x) < degree of g(x)
Degree of a polynomial is the highest power
of the variable in the polynomial.
(i (i)
deg p(x) = deg
q(x)
Degree of quotient will be equal to degree of dividend when divisor is constant ( i.e., when any polynomial is divided by a constant).
Thus, the division algorithm is satisfied. (iii)deg r(x) = 0
Degree of remainder will be 0 when remainder comes to a constant. Let us assume the division of x3+ 1by x2.
Here, p(x) = x3 + 1
g(x) = x2
q(x) = x and
r(x) = 1
Clearly, the degree of r(x)
is 0.
Checking for division algorithm,
p(x) = g(x)
× q(x) + r(x) x3 + 1 = (x2
)
× x + 1
x3 + 1 = x3 + 1
Thus, the division algorithm is satisfied.
Exercise 2.4 : Solutions of Questions
Q1:
Q2 :
Q3:
- 5 - a = 0
Therefore, a = - 5
Hence, k = 5 and a = - 5
NCERT Solutions for Class 10 Mathematics (10th) Chapter 2: Polynomials
Concepts covered in Polynomials are Concept of Irrational Numbers, Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, Fundamental Theorem of Arithmetic Motivating Through Examples, Introduction of Polynomials, Proofs of Irrationality, Rational Numbers and Their Decimal Expansions, Polynomials Examples and Solutions.
NCERT Solutions Class 10 Maths Chapter 2 Polynomials
NCERT solutions for class 10 maths Chapter 2 Polynomials encompasses essential concepts around Polynomials such as Euclid’s division lemma, Prime Numbers, Composite Numbers, Fundamental Theorem of Arithmetic, HCF, and LCM by Prime Factorization Method, and Irrational Numbers. Polynomials are the combination of rational and irrational numbers. They are denoted by the symbol "R" and can be both positive and negative. NCERT solutions class 10 maths Chapter 2 will help cover all the relevant concepts of Polynomials as it has significant applications in real life. Kids also learn about important facts such as the use of the Fundamental Theorem of Arithmetic in proving the irrationality of many of the numbers and exploring when exactly the decimal expansion of a rational number is terminating and when it is non terminating. As numbers form the foundation of Mathematics, understanding the basics is a must.
In this chapter, students will also learn how to represent the Polynomials on a number line and the process of successive magnification, which is used to represent a decimal expansion on a number line. The lesson combines certain concepts that kids have come across in previous classes with newer complicated topics to give them a holistic understanding of Polynomials and their application. The Class 10 Maths NCERT Solutions Chapter 2 can be found in the pdf format below and also you can find some of these in the exercises given below.
NCERT Solutions for Class 10 Maths Chapter 2 PDF
Mathematics presents us with a variety of numbers and Polynomials are one of them. In order to understand higher mathematics, it makes sense to first take a look at the number system in detail which has been achieved in this book. An interesting aspect of the NCERT book is that it details some historical notes, cutting the monotony of studies. Further, the solutions have certain tips and tricks to help a child streamline his process of learning. The links for NCERT Solutions Class 10 Maths available for free PDF download are given below:
Download Class 10 Maths NCERT Solutions Chapter 2 Polynomials with PDF and Video Class
Dear Students, Here we provide you the best and accurate Class Ten CBSE NCERT Maths Second Chapter Solutions. Here we also provide you some important video classes and Valuable PDF File, that can help you perform better in your life. Students, you know that this “Polynomials” chapter is most important for your examination perpective.
List of Formulas in NCERT Solutions Class 10 Maths Chapter 2 Polynomials
NCERT solutions Class 10 maths Chapter 2 covers the formulas based on the properties of Polynomials and their theorems. These formulas will help the students solve questions accurately and quickly. They are not just helpful for class 10, but higher-level mathematics as well. Apart from these, it is necessary for kids to remember certain points related to a particular category of numbers. For example, the decimal expansion of an irrational number is non-terminating and non-repeating. Let us go through some of the formulas and properties covered in NCERT Solutions Class 10 Maths Chapter 2 Polynomials.
Important Questions for Class 10 Maths NCERT Solutions Chapter 2
In this “Polynomials” chapter many questions are very very important for your exam, so we fully discussed those important questions. In this Second Chapter some more important questions are below, please practice these questions and match your answer with our answer key.
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