NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials. Furthermore, here we’ve provided you with the latest solution for Class 10 CBSE NCERT Maths Chapter 2 Polynomials. As a result here you’ll find solutions to all the exercises. This NCERT Class 10 solution will help you to score good marks in your exam.
What is a Polynomial?
The Chapter 2 of Class 10 Maths is Polynomials. Moreover, Polynomial is an algebraic expression consisting of variables, and coefficients, with various mathematical operations like addition, subtraction, multiplication, and non-negative integer exponentiation.
Types of Polynomials
The different types of Polynomials are as follows: Monomial, Binomial, and Trinomial.
Monomials: Monomials are the algebraic expression with only one like term or variable. For example 6x + 9x + 5x. Since all the terms or variables are the same and are having the same power. Hence these are called Monomials. `
Binomials: Binomials are the algebraic expression with two, unlike terms or variables. For example 6x + 9x2 is binomial as there are two unlike terms in the expression. Furthermore, 6x + 9y is also a binomial.
Trinomials: Trinomials are the algebraic expression with three, unlike terms or variables. For example 6x + 9x2 + 10x3 is trinomial as there are three unlike terms in the expression. Furthermore, 6x + 9y + 10z is also a trinomial.
Students can refer to our solution for Polynomials. The Chapter 2 Solution of NCERT will help students prepare for the exams and easily crack the exam.
Exercise wise solution
- Chapter 2 Polynomials Solution for Ex 2.1
- Chapter 2 Polynomials Solution for Ex 2.2
- Chapter 2 Polynomials Solution for Ex 2.3
- Chapter 2 Polynomials Solution for Ex 2.4
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.1
Exercise 2.1: Solutions of Questions on Page Number: 28
The graphs of y = p(x) are given in the following figure, for some polynomials p(x). Find the number of zeroes of(x), in each case.
Answer:
- The number of zeroes is 0 as the graph does not cut the x-axis at any point.
- The number of zeroes is 1 as the graph intersects the x-axis at only 1 point.
- The number of zeroes is 3 as the graph intersects the x-axis at 3 points.
- The number of zeroes is 2 as the graph intersects the x-axis at 2 points.
- The number of zeroes is 4 as the graph intersects the x-axis at 4 points.
- The number of zeroes is 3 as the graph intersects the x-axis at 3 points.
NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.2
Exercise 2.2: Solutions of Questions on Page Number: 33
Q1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
Ans:
Q2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Answer:
NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.3
Exercise 2.3: Solutions of Questions on Page Number: 36
Q1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
Quotient = x2 + x – 3
Remainder = 8
Quotient = – x2 – 2
Remainder = -5x +10
Q2. Verify that the numbers given alongside the cubic polynomials below are their zeroes. Also, verify the relationship between the zeroes and the coefficients in each case:
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
Q5
Q6.
Q7. Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
- deg p(x) = deg q(x)
- deg q(x) = deg r(x)
- 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.
- 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).
(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.
NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4
Exercise 2.4 : Solutions of Questions on Page Number : 37
Q1.
Q2.
Answer:
Q3.
Answer:
– 5 – a = 0
Therefore, a = – 5 Hence, k = 5 and a = – 5
NCERT Class 10 Maths All Chapters Solution
Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equation in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progressions
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry
Chapter 9: Some Applications of Trigonometry
Chapter 10: Circles
Chapter 11: Constructions
Chapter 12: Areas Related to Circles
Chapter 13: Surface Areas and Volumes
Chapter 14: Statistics
Chapter 15: Probability