NCERT Solutions for Class 10 Maths Chapter 2 Polynomials
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials - In this chapter, you will learn about the polynomials with any degree and its solutions using a graphical representation. The NCERT Solutions for Class 10 Maths Chapter 2 Polynomials gives a detailed explanation of questions given in the NCERT Book of Class 10 Maths. You must refer to these NCERT solutions to check the correct answers and proper explanation of each question. These NCERT Solutions for Class 10 Maths Chapter 2 Polynomials are prepared by experts and are easy understand. You can check the NCERT solutions for Class 10 for other subjects here.
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NCERT Solutions for Class 10 Maths Chapter 2 - Topics
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 for other chapters
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | NCERT solutions for class 10 maths chapter 2 Polynomials |
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 |
Features of NCERT Solutions for Class 10 Maths Chapter 2 Polynomials
The NCERT Class 10 maths solutions chapter 2 are important for board exams as well as for competitive exams.
These NCERT solutions are prepared by experts. These solutions are very well explained and are to the point.
To make the solutions easy to understand, relevant diagrams or images are given with the solutions wherever required.
You can check these solutions online or can save the webpage to get these solutions offline. NCERT Solutions for Class 10 Maths Chapter 2 PDF download will also be made available soon.
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 Class 10 Maths chapter 2 NCERT solutions, 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.
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 does not provide the marks distributions chapter-wise but it provides the total weightage of a unit. As per CBSE the total weightage of algebra (4 chapters) is 20 marks in the final board exam.
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: How many chapters are there in class 10 maths?
Answer:
There are 15 chapters in the class 10 maths NCERT.
Question: How are the NCERT solutions helpful in the board exam?
Answer:
NCERT solutions are provided in a detailed manner, 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
Board cbse class 10 Is cancelled and promote all student please sir because of corona do not study
Hello aspirant,
No CBSE and ICSE board didn't not cancelled the 10th and 12th exam.
As they had declared that 10th and 12th class exam will not be cancelled and students will have to give it in offline mode in this pandemic also.
Hope this helps you
All the best for your future
CBSE class 10th malayalam can someone please tell me a good one
Hello Dear,
Malayalam is the mother tongue of those who have their roots in Kerala. It is one of the Dravidian languages that has similarities in words with its other contemporary languages such as Tamil and Telugu. People who speak Malayalam are referred to as Mallus. You can download the previous year papers from the link below:
https://school.careers360.com/download/sample-papers/cbse-10th-class-malayalam-solved-sample-paper-2021
Good Luck
When will the Karnataka NTSE Stage 1 Merit list(i.e people who have cleared stage-1) and the cut off come out?
DSERT, Karnataka has released the NTSE Karnataka 2021 Result stage 1 on March 9, 2021 on their official website ( dsert.kar.nic.in ). It is available in the form of district-wise marks lists , consisting of registration numbers and marks of all students.
Along with the NTSE stage 1 result, cutoff and merit list of selected candidates is also released.
The students those who have cleared the stage 1 exam are eligible to seat for the stage 2 exam which is going to be held on June 13, 2021 . The scholarship will be given to the students who will pass the stage 2 examination.
To know more about NTSE Karnataka Important Dates, Cut-off, Scholarship visit :
https://www.google.com/amp/s/school.careers360.com/articles/ntse-karnataka-result/amp
Hope it helps
Thank You !!!
Age criteria to appear in class 10 CBSE exam
Hello Bishal
According to guidelines of CBSE, minimum age to appear for class x must be 14 years. There is no upper limit to appear for class x cbse board.
A candidate can appear for maximum three attempts.
Some candidates give private exams or sometimes students fail in standard ix then they privately appear for class x then their age must be more than 14 years. Sometimes students appear for x class after one year gap of passing class ix then also their age would be 15 or 16 as there is no upper limit age.
My child is supposed to make another attempt at compartment exam of 10th cbse Missed last date for applying. since the boards are postponed to May 4th can I pay her fees and apply now.
Hello sir I'm sorry to inform you but now you're not eligible to fill the registration form as last date to fill the registration Form was 9th December 2020. Yes examination gets postponed to May but portal to fill the registration form is not open , in case if the registration form portal will open again you can fill the registration form and make the payment.
Feel free to comment if you've any doubt
Good luck