NCERT Solutions for Class 10 Maths Chapter 2 Polynomials
NCERT solutions for class 10 maths chapter 2 Polynomials - In the previous class, you have already studied the polynomial with one degree. In class 10 maths chapter 2 you will study the polynomials with any degree and its solutions using graphical representation. NCERT solutions for class 10 maths chapter 2 Polynomials have detailed explanations to each and every question. A polynomial is constructed using variables and numbers using addition, subtraction, multiplication, and division. When two polynomials are divided then the resultant is called the rational expression of polynomials. NCERT solutions for class 10 maths chapter 2 Polynomials is an important tool to score high in the board examinations. Polynomial is an important part of algebra in which we get the knowledge about the various operation performed over polynomials. Polynomials are further classified according to their degrees. A degree in the polynomials is the highest power of variable present in the equation. Let's understand the degree by taking some examples-
In the equations, the maximum power of the variables is 1 and 2 respectively. So the degree for the polynomials is 1 and 2 respectively. Polynomials with degrees 1, 2, 3 are known as linear, quadratic and cubic polynomials respectively. NCERT solutions for class 10 maths chapter 2 Polynomials is covering each question in a detailed manner. Apart from this particular chapter, you can also download the solutions class-wise and subject wise by clicking on the link where NCERT solutions are there. Here you will get NCERT solutions for class 10 also.
Types of questions asked from class 10 maths chapter 2 Polynomials
The degree of a polynomial
Number of zeroes in a quadratic polynomial
The sum & product of quadratic polynomial
Division algorithm
The number of zeroes in a cubic polynomial
NCERT solutions for class 10 maths chapter 2 Polynomials Excercise: 2.1
Answer:
The number of zeroes of p(x) is zero as the curve does not intersect the x-axis.
Answer:
The number of zeroes of p(x) is one as the graph intersects the x-axis only once.
Answer:
The number of zeroes of p(x) is three as the graph intersects the x-axis thrice.
Answer:
The number of zeroes of p(x) is two as the graph intersects the x-axis twice.
Answer:
The number of zeroes of p(x) is four as the graph intersects the x-axis four times.
Answer:
The number of zeroes of p(x) is three as the graph intersects the x-axis thrice.
NCERT solutions for class 10 maths chapter 2 Polynomials Excercise: 2.2
Answer:
x ^{ 2 } - 2x - 8 = 0
x ^{ 2 } - 4x + 2x - 8 = 0
x(x-4) +2(x-4) = 0
(x+2)(x-4) = 0
The zeroes of the given quadratic polynomial are -2 and 4
VERIFICATION
Sum of roots:
Verified
Product of roots:
Verified
Answer:
The zeroes of the given quadratic polynomial are 1/2 and 1/2
VERIFICATION
Sum of roots:
Verified
Product of roots:
Verified
Answer:
6x ^{ 2 } - 3 - 7x = 0
6x ^{ 2 } - 7x - 3 = 0
6x ^{ 2 } - 9x + 2x - 3 = 0
3x(2x - 3) + 1(2x - 3) = 0
(3x + 1)(2x - 3) = 0
The zeroes of the given quadratic polynomial are -1/3 and 3/2
Sum of roots:
Verified
Product of roots:
Verified
Answer:
4u ^{ 2 } + 8u = 0
4u(u + 2) = 0
The zeroes of the given quadratic polynomial are 0 and -2
VERIFICATION
Sum of roots:
Verified
Product of roots:
Verified
Answer:
t ^{ 2 } - 15 = 0
The zeroes of the given quadratic polynomial are and
VERIFICATION
Sum of roots:
Verified
Product of roots:
Verified
Answer:
3x ^{ 2 } - x - 4 = 0
3x ^{ 2 } + 3x - 4x - 4 = 0
3x(x + 1) - 4(x + 1) = 0
(3x - 4)(x + 1) = 0
The zeroes of the given quadratic polynomial are 4/3 and -1
VERIFICATION
Sum of roots:
Verified
Product of roots:
Verified
Answer:
The required quadratic polynomial is
Answer:
The required quadratic polynomial is
Answer:
The required quadratic polynomial is x ^{ 2 } + .
Answer:
The required quadratic polynomial is x ^{ 2 } - x + 1
Answer:
The required quadratic polynomial is 4x ^{ 2 } + x + 1
Answer:
The required quadratic polynomial is x ^{ 2 } - 4x + 1
NCERT solutions for class 10 maths chapter 2 Polynomials Excercise: 2.3
Answer:
The polynomial division is carried out as follows
The quotient is x-3 and the remainder is 7x-9
Answer:
The division is carried out as follows
The quotient is
and the remainder is 8
Answer:
The polynomial is divided as follows
The quotient is and the remainder is
Answer:
After dividing we got the remainder as zero. So is a factor of
Answer:
To check whether the first polynomial is a factor of the second polynomial we have to get the remainder as zero after the division
After division, the remainder is zero thus is a factor of
Answer:
The polynomial division is carried out as follows
The remainder is not zero, there for the first polynomial is not a factor of the second polynomial
Q3 Obtain all other zeroes of , if two of its zeroes are
Answer:
Two of the zeroes of the given polynomial are .
Therefore two of the factors of the given polynomial are and
is a factor of the given polynomial.
To find the other factors we divide the given polynomial with
The quotient we have obtained after performing the division is
(x+1) ^{ 2 } = 0
x = -1
The other two zeroes of the given polynomial are -1.
Answer:
Quotient = x-2
remainder =-2x+4
Carrying out the polynomial division as follows
Answer:
deg p(x) will be equal to the degree of q(x) if the divisor is a constant. For example
Q5 (2) Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and deg q(x) = deg r(x)
Answer:
Example for a polynomial with deg q(x) = deg r(x) is given below
Answer:
example for the polynomial which satisfies the division algorithm with r(x)=0 is given below
NCERT solutions for class 10 maths chapter 2 Polynomials Excercise: 2.4
Answer:
p(x) = 2x ^{ 3 } + x ^{ 2 } -5x + 2
p(1) = 2 x 1 ^{ 3 } + 1 ^{ 2 } - 5 x 1 + 2
p(1) =2 + 1 - 5 + 2
p(1) = 0
p(-2) = 2 x (-2) ^{ 3 } + (-2) ^{ 2 } - 5 x (-2) +2
p(-2) = -16 + 4 + 10 + 2
p(-2) = 0
Therefore the numbers given alongside the polynomial are its zeroes
Verification of relationship between the zeroes and the coefficients
Comparing the given polynomial with ax ^{ 3 } + bx ^{ 2 } + cx + d, we have
a = 2, b = 1, c = -5, d = 2
The roots are
Verified
Verified
Verified
Answer:
p(x) = x ^{ 3 } - 4x ^{ 2 } + 5x - 2
p(2) = 2 ^{ 3 } - 4 x 2 ^{ 2 } + 5 x 2 - 2
p(2) = 8 - 16 + 10 - 2
p(-2) = 0
p(1) = 1 ^{ 3 } - 4 x 1 ^{ 2 } + 5 x 1 - 2
p(1) = 1 - 4 + 5 - 2
p(1) = 0
Therefore the numbers given alongside the polynomial are its zeroes
Verification of relationship between the zeroes and the coefficients
Comparing the given polynomial with ax ^{ 3 } + bx ^{ 2 } + cx + d, we have
a = 1, b = -4, c = 5, d = -2
The roots are
Verified
Verified
Verified
Answer:
Let the roots of the polynomial be
Hence the required cubic polynomial is x ^{ 3 } - 2x ^{ 2 } - 7x + 14 = 0
Q3 If the zeroes of the polynomial are a – b, a, a + b, find a and b.
Answer:
The roots of the above polynomial are a, a - b and a + b
Sum of the roots of the given plynomial = 3
a + (a - b) + (a + b) = 3
3a = 3
a = 1
The roots are therefore 1, 1 - b and 1 + b
Product of the roots of the given polynomial = -1
1 x (1 - b) x (1 + b) = - 1
1 - b ^{ 2 } = -1
b ^{ 2 } - 2 = 0
Therefore a = 1 and .
Q4 If two zeroes of the polynomial are , find other zeroes .
Answer:
Given the two zeroes are
therefore the factors are
We have to find the remaining two factors. To find the remaining two factors we have to divide the polynomial with the product of the above factors
Now carrying out the polynomial division
Now we get
So the zeroes are
Answer:
The polynomial division is carried out as follows
Given the remainder =x+a
The obtained remainder after division is
now equating the coefficient of x
which gives the value of
now equating the constants
Therefore k=5 and a=-5
NCERT solutions for class 10 maths chapter wise
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | NCERT solutions for class 10 maths chapter 3 Pair of Linear Equations in Two Variables |
Chapter 4 | NCERT solutions for class 10 maths chapter 4 Quadratic Equations |
Chapter 5 | NCERT solutions for class 10 chapter 5 Arithmetic Progressions |
Chapter 6 | |
Chapter 7 | NCERT solutions for class 10 maths chapter 7 Coordinate Geometry |
Chapter 8 | NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry |
Chapter 9 | NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | NCERT solutions for class 10 chapter maths chapter 12 Areas Related to Circles |
Chapter 13 | NCERT solutions class 10 maths chapter 13 Surface Areas and Volumes |
Chapter 14 | |
Chapter 15 |
NCERT solutions of class 10 subject wise
How to use NCERT solutions for class 10 maths chapter 2 polynomials ?
You will find yourself much improved in terms of concepts, their applications, and problem-solving. 90% of the questions in the board examinations come from the NCERT syllabus.
Now when you have gone through the NCERT solutions for class 10 maths chapter 2 polynomials, you must have learnt to answer a question in the step by step manner.
Once you have studied the NCERT solutions for class 10, your next target should be previous year questions papers.
NCERT syllabus coverage and previous year papers are enough tools to get a good score in the board examination. After going through these two things, you can jump to the next chapters.
Keep working hard & happy learning!
Frequently Asked Question (FAQs) - NCERT Solutions for Class 10 Maths Chapter 2 Polynomials
Question: What is the weightage of the chapter polynomials for CBSE board exam ?
Answer:
CBSE doesn't provides the marks distributions chapter-wise but it provides the total weightage of a unit( upto 4-5 chapters). As per CBSE the total weightage of algebra ( 4 chapters) is 20 marks in the final board exam.
Question: Where can I find the complete solutions of NCERT class 10 maths ?
Answer:
Here you will get the detailed NCERT solutions for class 10 maths by clicking on the link.
Question: What are the important topics of the class 10 maths chapter 2 polynomials ?
Answer:
Polynomial and it's definition, degree of a polynomial, number of zeroes in a quadratic polynomial, sum & product of quadratic polynomial, division algorithm, number of zeroes in a cubic polynomial are important topics from the chapter polynomials.
Question: Which is the official website of NCERT ?
Answer:
http://ncert.nic.in/ is the official website of the NCERT where you can get NCERT textbooks from class 1 to 12 and syllabus from class 1 to 12 for all the subjects.
Question: How many chapters are there in the class 10 maths ?
Answer:
There are 15 chapters in the class 10 maths NCERT. Chapter 1- Real Numbers, Chapter 2- Polynomials, Chapter 3- Pair of Linear Equations 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 are the chapters in the NCERT class 10 maths.
Question: How the NCERT solutions are helpful in the board exam ?
Answer:
NCERT solutions are very important, if have stuck into any problem while solving them. These solutions are provided in a detailed manners, so it will be very easy for you to understand the concept. You can also use them for quick revision before the board exam.
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Questions related to CBSE Class 10th
I got 85% in CBSE class 10th , I am from open category. on the basis of merit list can I get admission in government polytechnic college, Aurangabad for computer science
Government Polytechnic College Aurangabad is a public college which was established in the year 1955. It has student capacity of 2042 students and has 87 faculty members.
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For more information please check the link below: https://www.careers360.com/colleges/government-polytechnic-aurangabad/amp
but I think I can rewrite the paper
Hello Aspirant,
If you are talking about the CBSE class 10th exams and you have already appeared for the exams and are willing to re-appear . The reason mentioned by you is not clear and so I am supposing that this is because , you have got less/unexpected marks in your exams. To be honest, it's really difficult for you to rewrite the paper in this pandemic situation where every school and college is closed yet.
I would ask you to check out once our country deals effectively with the virus and the vaccine is out, then only something can be said with surety, until then it's just the assumptions.
Hope that helps
Stay safe
All the best.
I not satisfied in only one subject is this wrong or correct to go for re-vaulution
Dear Student,
If you are totally confident about this subject then go for re-valuation. At first talk to your school or college authority about this and after being sure and knowing all the things then apply for this. May it will help you.
Thank You.
CBSE class 10th compartment online forms Apply 2020
Hello,
CBSE Class 10th compartment result is provided through the official website: cbseresults.nic.in. Students failing in a subject in annual exams of CBSE will be able to apply for compartment exam in the third week of August 2020. Last date to submit CBSE 10th compartment form is third week of August 2020. Please click the below link to know more.
https://school.careers360.com/articles/cbse-compartment-result-10th-class
result 10th cbse ka chahiye or uska marksheet bhee
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Students can also check their results through Umang and DigiLocker app. http://news.careers360.com/cbse-10th-result-2020-live-updates-check-cbse-class-10-results-cbseresultsnicin