#### Online Mock Tests

#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Liner Equation in Two Variable

Chapter 4: Quadatric Euation

Chapter 5: Arithematic Progressions

Chapter 6: Triangles

Chapter 7: Coordinate Geometry

Chapter 8: Introduction to Trignometry & its Equation

Chapter 9: Circles

Chapter 10: Construction

Chapter 11: Area Related To Circles

Chapter 12: Surface Areas and Volumes

Chapter 13: Statistics and Probability

## Chapter 2: Polynomials

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

If one of the zeroes of the quadratic polynomial (k – 1)x^{2} + k x + 1 is – 3, then the value of k is ______.

`4/3`

`(-4)/3`

`2/3`

`(-2)/3`

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`

If the zeroes of the quadratic polynomial x^{2} + (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

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

1

2

3

More than 3

Given that one of the zeroes of the cubic polynomial ax^{3} + bx^{2} + cx + d is zero, the product of the other two zeroes is ______.

`- c/a`

`c/a`

0

`- b/a`

If one of the zeroes of the cubic polynomial x^{3} + ax^{2} + 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

The zeroes of the quadratic polynomial x^{2} + 99x + 127 are ______.

Both positive

Both negative

One positive and one negative

Both equal

The zeroes of the quadratic polynomial x^{2} + kx + k, k ≠ 0 ______.

Cannot both be positive

Cannot both be negative

Are always unequal

Are always equal

If the zeroes of the quadratic polynomial ax^{2} + 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

If one of the zeroes of a quadratic polynomial of the form x^{2} + 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

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

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

#### Answer the following and justify:

Can x^{2} – 1 be the quotient on division of x^{6} + 2x^{3} + x – 1 by a polynomial in x of degree 5?

What will the quotient and remainder be on division of ax^{2} + bx + c by px^{3} + qx^{2} + rx + s, p ≠ 0?

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)?

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)?

Can the quadratic polynomial x^{2} + kx + k have equal zeroes for some odd integer k > 1?

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

If the zeroes of a quadratic polynomial ax^{2} + bx + c are both positive, then a, b and c all have the same sign.

True

False

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

True

False

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

True

False

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

True

False

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

If all three zeroes of a cubic polynomial x^{3} + ax^{2} – bx + c are positive, then at least one of a, b and c is non-negative.

True

False

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

True

False

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 2 Polynomials Exercise 2.3 [Pages 12 - 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} – 3x – 1

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

3x^{2} + 4x – 4

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

5t^{2} + 12t + 7

t^{3} – 2t^{2} – 15t

`2x^2 + (7/2)x + 3/4`

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

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

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

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

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

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

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`

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`

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`

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

Given that the zeroes of the cubic polynomial x^{3} – 6x^{2} + 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.

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.

Find k so that x^{2} + 2x + k is a factor of 2x^{4} + x^{3} – 14 x^{2} + 5x + 6. Also find all the zeroes of the two polynomials.

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.

For which values of a and b, are the zeroes of q(x) = x^{3} + 2x^{2} + a also the zeroes of the polynomial p(x) = x^{5} – x^{4} – 4x^{3} + 3x^{2 }+ 3x + b? Which zeroes of p(x) are not the zeroes of q(x)?

## Chapter 2: Polynomials

## 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.

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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.

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