NCERT solutions for Mathematics [English] Class 10 chapter 2 - Polynomials [2018 edition]

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 the following.

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

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

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

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

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

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

x² – 2x – 8

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

4s² – 4s + 1

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

6x² – 3 – 7x

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

4u² + 8u

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

t² – 15

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

3x² – x – 4

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

`1/4 , -1`

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

`sqrt2 , 1/3`

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

`0, sqrt5`

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

1, 1

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

`-1/4 ,1/4`

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

4, 1

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

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

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

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

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

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

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

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)

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

deg p(x) = deg q(x)

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

deg q(x) = deg r(x)

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

deg r(x) = 0

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`

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

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

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

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

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.