# Class 10 Maths NCERT Solutions Chapter 2 Polynomials

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials are part of NCERT Solutions for Class 10 Maths. Here we have given Maths NCERT Solutions Class 10 Chapter 2 Polynomials.

### Class 10 Maths NCERT Solutions Chapter 2 Polynomials Ex 2.1

Question 1:

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

Solution:

### Class 10 Maths NCERT Solutions Chapter 2 Polynomials Ex 2.2

Question 1.

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

(i) x^{2} – 2x – 8

(ii) 4s^{2} – 4s + 1

(iii) 6x^{2} – 3 – 7x

(iv) 4u^{2} + 8u

(v) t^{2} – 15

(vi) 3x^{2} – x – 4

Solution:

Question 2.

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

Solution:

### Class 10 Maths NCERT Solutions Chapter 2 Polynomials Ex 2.3

Question 1.

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

(i) p(x) = x^{3} – 3x^{2} + 5x – 3, g(x) = x^{2} – 2

(ii) p(x) = x^{4} – 3x^{2} + 4x + 5, g(x) = x^{2} + 1 – x

(iii) p(x) = x^{4}– 5x + 6, g(x) = 2 – x^{2
Solution:
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Question 2.

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

(i) t^{2} – 3, 2t^{4} + 3t^{3} – 2t^{2}– 9t – 12

(ii) x^{2} + 3x + 1, 3x^{4} + 5x^{3} – 7x^{2} + 2x + 2

(iii) x^{2} + 3x + 1, x^{5} – 4x^{3 }+ x^{2} + 3x + 1

Solution:

Question 3.

Obtain all other zeroes of 3x^{4} + 6x^{3} – 2x^{2} – 10x – 5, if two of its zeroes are and

Solution:

Question 4.

On dividing x^{3 }– 3x^{2} + x + 2bya polynomial g(x), the quotient and remainder were x – 2 and -2x + 4 respectively. Find g(x).

Solution:

Question 5.

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

(i) deg p(x) = deg q(x)

(ii) deg q(x) = deg r(x)

(iii) deg r(x) = 0

Solution:

### Class 10 Maths NCERT Solutions Chapter 2 Polynomials Ex 2.4

Question 1.

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:

(i) 2x^{3} + x^{2} – 5x + 2;

(ii) x^{3} – 4x^{2} + 5x – 2; 2, 1, 1

Solution:

Question 2.

Find a cubic polynomial with the sum, some of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.

Solution:

Question 3.

If the zeroes of the polynomial x^{3} – 3x^{2} + x + 1 are a-b, a, a + b, find a and b.

Solution:

Question 4.

If two zeroes of the polynomial x^{4} – 6x^{3} – 26x^{2 }+ 138x – 35 are 2 ± √3, find other zeroes.

Solution:

Question 5.

If the polynomial x^{4} – 6x^{3} + 16x^{2} – 25x + 10 is divided by another polynomial x^{2} – 2x + k, the remainder comes out to be x + a, find k and a.

Solution: