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NCERT solutions Mathematics Class 10 chapter 2 Polynomials

Chapters

NCERT Mathematics Class 10

Mathematics Textbook for Class 10

Chapter 2 - Polynomials

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 1.1 | 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)

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

Page 33

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

x2 – 2x – 8

Q 1.1 | 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 1.2 | Page 33

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

6x2 – 3 – 7x

Q 1.3 | Page 33

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

4u2 + 8u

Q 1.4 | Page 33

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

t2 – 15

Q 1.5 | Page 33

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

3x2 – x – 4

Q 1.6 | Page 33

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

`1/4 , -1`

Q 2.1 | Page 33

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

`sqrt2 , 1/3`

Q 2.2 | Page 33

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

`0, sqrt5`

Q 2.3 | Page 33

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

1, 1

Q 2.4 | 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 2.5 | Page 33

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

4, 1

Q 2.6 | Page 33

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 1.1 | 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) = x4 – 3x2 + 4x + 5,   g(x) = x2 + 1 – x

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 – 5x + 6, g(x) = 2 – x2

Q 1.3 | 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 2.1 | 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 2.2 | 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 2.3 | 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 3 | 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 4 | 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 5.1 | 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 5.2 | Page 36

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

deg r(x) = 0

Q 5.3 | Page 36

Pages 36 - 37

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 1.1 | 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 1.2 | 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 2 | Page 36

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

Q 3 | Page 37

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

Q 4 | 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.

Q 5 | Page 37

Extra questions

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

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 4x2 - 9 and verify the relation between the zeros and its coffiecents.

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

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

NCERT Mathematics Class 10

Mathematics Textbook for Class 10
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