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NCERT solutions for Mathematics Exemplar Class 10 chapter 2 - Polynomials [Latest edition]

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Chapter 2: Polynomials

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4
Exercise 2.1 [Pages 9 - 10]

NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.1 [Pages 9 - 10]

Exercise 2.1 | Q 1 | Page 9

If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is – 3, then the value of k is ______.

  • `4/3`

  • `(-4)/3`

  • `2/3`

  • `(-2)/3`

Exercise 2.1 | Q 2 | Page 9

A quadratic polynomial, whose zeroes are –3 and 4, is ______.

  • `x^2 - x + 12`

  • `x^2 + x + 12`

  • `x^2/2 - x/2 - 6`

  • `2x^2 + 2x - 24`

Exercise 2.1 | Q 3 | Page 9

If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then ______.

  • a = –7, b = –1

  • a = 5, b = –1

  • a = 2, b = – 6

  • a = 0, b = – 6

Exercise 2.1 | Q 4 | Page 9

The number of polynomials having zeroes as –2 and 5 is ______.

  • 1

  • 2

  • 3

  • More than 3

Exercise 2.1 | Q 5 | Page 9

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.

  • `- c/a`

  • `c/a`

  • 0

  • `- b/a`

Exercise 2.1 | Q 6 | Page 9

If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is ______.

  • b – a + 1

  • b – a – 1

  • a – b + 1

  • a – b –1

Exercise 2.1 | Q 7 | Page 10

The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.

  • Both positive

  • Both negative

  • One positive and one negative 

  • Both equal

Exercise 2.1 | Q 8 | Page 10

The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0 ______.

  • Cannot both be positive

  • Cannot both be negative

  • Are always unequal

  • Are always equal

Exercise 2.1 | Q 9 | Page 10

If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.

  • c and a have opposite signs

  • c and b have opposite signs

  • c and a have the same sign

  • c and b have the same sign

Exercise 2.1 | Q 10 | Page 10

If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.

  • Has no linear term and the constant term is negative

  • Has no linear term and the constant term is positive

  • Can have a linear term but the constant term is negative

  • Can have a linear term but the constant term is positive

Exercise 2.1 | Q 11 | Page 10

Which of the following is not the graph of a quadratic polynomial?

Exercise 2.2 [Pages 11 - 12]

NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.2 [Pages 11 - 12]

Answer the following and justify:

Exercise 2.2 | Q 1.(i) | Page 11

Can x2 – 1 be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5?

Exercise 2.2 | Q 1.(ii) | Page 11

What will the quotient and remainder be on division of ax2 + bx + c by px3 + qx2 + rx + s, p ≠ 0?

Exercise 2.2 | Q 1.(iii) | Page 11

If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?

Exercise 2.2 | Q 1.(iv) | Page 11

If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?

Exercise 2.2 | Q 1.(v) | Page 11

Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?

Are the following statements ‘True’ or ‘False’? Justify your answers.

Exercise 2.2 | Q 2.(i) | Page 11

If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.

  • True

  • False

Exercise 2.2 | Q 2.(ii) | Page 11

If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.

  • True

  • False

Exercise 2.2 | Q 2.(iii) | Page 11

If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.

  • True

  • False

Exercise 2.2 | Q 2.(iv) | Page 11

If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

  • True

  • False

Exercise 2.2 | Q 2.(v) | Page 12

If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

  • True

  • False

Exercise 2.2 | Q 2.(vi) | Page 12

If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.

  • True

  • False

Exercise 2.2 | Q 2.(vii) | Page 12

The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`

  • True

  • False

Exercise 2.3 [Pages 12 - 13]

NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.3 [Pages 12 - 13]

Exercise 2.3 | Q 1.(i) | Page 12

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

4x2 – 3x – 1

Exercise 2.3 | Q 1.(ii) | Page 12

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

3x2 + 4x – 4

Exercise 2.3 | Q 1.(iii) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

5t2 + 12t + 7

Exercise 2.3 | Q 1.(iv) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

t3 – 2t2 – 15t

Exercise 2.3 | Q 1.(v) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`2x^2 + (7/2)x + 3/4`

Exercise 2.3 | Q 1.(vi) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`4x^2 + 5sqrt(2)x - 3`

Exercise 2.3 | Q 1.(vii) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`

Exercise 2.3 | Q 1.(viii) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`v^2 + 4sqrt(3)v - 15`

Exercise 2.3 | Q 1.(ix) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`y^2 + 3/2 sqrt(5)y - 5`

Exercise 2.3 | Q 1.(x) | Page 13

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`7y^2 - 11/3 y - 2/3`

Exercise 2.4 [Pages 14 - 15]

NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.4 [Pages 14 - 15]

Exercise 2.4 | Q 1.(i) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`(-8)/3, 4/3`

Exercise 2.4 | Q 1.(ii) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`21/8, 5/16`

Exercise 2.4 | Q 1.(iii) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`-2sqrt(3), -9`

Exercise 2.4 | Q 1.(iv) | Page 14

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`(-3)/(2sqrt(5)), -1/2`

Exercise 2.4 | Q 2 | Page 14

Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.

Exercise 2.4 | Q 3 | Page 15

Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.

Exercise 2.4 | Q 4 | Page 15

Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.

Exercise 2.4 | Q 5 | Page 15

Given that `x - sqrt(5)` is a factor of the cubic polynomial `x^3 - 3sqrt(5)x^2 + 13x - 3sqrt(5)`, find all the zeroes of the polynomial.

Exercise 2.4 | Q 6 | Page 15

For which values of a and b, are the zeroes of q(x) = x3 + 2x2 + a also the zeroes of the polynomial p(x) = x5 – x4 – 4x3 + 3x2 + 3x + b? Which zeroes of p(x) are not the zeroes of q(x)?

Chapter 2: Polynomials

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4
Mathematics Exemplar Class 10 - Shaalaa.com

NCERT solutions for Mathematics Exemplar Class 10 chapter 2 - Polynomials

NCERT solutions for Mathematics Exemplar Class 10 chapter 2 (Polynomials) include all questions with solution and detail explanation. 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 the CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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

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

Using NCERT Class 10 solutions Polynomials exercise 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.

Get the free view of chapter 2 Polynomials Class 10 extra questions for Mathematics Exemplar Class 10 and can use Shaalaa.com to keep it handy for your exam preparation

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