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NCERT solutions for Class 10 Mathematics chapter 2 - Polynomials

Chapter 2 - Polynomials

Page 28

Q 1.1 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case

Q 1.2 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

Q 1.3 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

Q 1.4 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

Q 1.5 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

Q 1.6 | Page 28

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x)

Page 33

Q 1.1 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

x2 – 2x – 8

Q 1.2 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

4s2 – 4s + 1

Q 1.2 | Page 33

find the zeroes of the quadratic polynomial x2 – 2x – 8 and verify a relationship between zeroes and its coefficients

Q 1.3 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

6x2 – 3 – 7x

Q 1.4 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

4u2 + 8u

Q 1.5 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

t2 – 15

Q 1.6 | Page 33

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

3x2 – x – 4

Q 2.1 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

1/4 , -1

Q 2.2 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

sqrt2 , 1/3

Q 2.3 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

0, sqrt5

Q 2.4 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

1, 1

Q 2.5 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

-1/4 ,1/4

Q 2.6 | Page 33

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

4, 1

Page 36

Q 1.1 | Page 36

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2

Q 1.2 | Page 36

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x) = x4 – 3x2 + 4x + 5,   g(x) = x2 + 1 – x

Q 1.3 | Page 36

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x4 – 5x + 6, g(x) = 2 – x2

Q 2.1 | Page 36

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

t2 – 3, 2t4 + 3t3 – 2t2 – 9t – 12

Q 2.2 | Page 36

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2

Q 2.3 | Page 36

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x3 – 3x + 1, x5 – 4x3 + x2 + 3x + 1

Q 3 | Page 36

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are sqrt(5/3) and - sqrt(5/3)

Q 4 | Page 36

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)

Q 5.1 | Page 36

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg p(x) = deg q(x)

Q 5.2 | Page 36

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg q(x) = deg r(x)

Q 5.3 | Page 36

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg r(x) = 0

Pages 36 - 37

Q 1.1 | Page 36

Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.

2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2

Q 1.2 | Page 36

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

x3 – 4x2 + 5x – 2; 2, 1, 1

Q 2 | Page 36

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

Q 3 | Page 37

If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b

Q 4 | Page 37

If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± sqrt3 , find other zeroes

Q 5 | Page 37

If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.

Extra questions

Find the zeros of the quadratic polynomial 9x2 - 5 and verify the relation between the zeros and its coefficients.

Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.

if α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify  the relation between zeros and its cofficients

Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c

Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.

NCERT solutions for Class 10 Mathematics chapter 2 - Polynomials

NCERT solutions for Class 10 Mathematics chapter 2 (Polynomials) include all questions with solution and detail explanation from Mathematics Textbook for Class 10. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has created the CBSE Mathematics Textbook for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. These NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 2 Polynomials are Geometrical Meaning of the Zeroes of a Polynomial, Division Algorithm for Polynomials, Polynomials Examples and Solutions, Introduction to Polynomials, Relationship Between Zeroes and Coefficients of a Polynomial.

Using NCERT solutions for Class 10 Mathematics by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer NCERT Textbook Solutions to score more in exam.

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