# NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.3

NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.3 Polynomials (10th Maths Ex. 2.3) PDF in Hindi Medium and English Medium download in PDF or View in Video Format free all solutions or study online for academic session 2020-2021. MP Board and UP Board students are also using the books same as NCERT textbooks, they also can use UP Board Solutions for Class 10 Maths Chapter 2 Exercise 2.3 form here. PDF format solutions and Videos solutions are given at the same place. If you don’t want to download these solutions, study online without downloading the contents. Class 10 Maths Solutions of all the chapters given in Offline Apps also which are updated on the basis of new Curriculum 2020-2021 for CBSE students as well as UP Board students who are using NCERT Books 2020-21.

Download (Exercise 2.3) in PDF format to use it offline or use online given below.

## NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.3

 Class: 10 Maths (English and Hindi Medium) Chapter 2: Exercise 2.3

### 10 Maths Chapter 2 Exercise 2.3 Solutions

NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.3 Polynomials English medium as well as Hindi Medium given below to download or use it online free for academic year 2020-21. The videos related to Class 10 Maths Chapter 2 is also given to use free. Visit to discussion forum to share your knowledge or ask your doubts.

• ### Class 10 Maths Exercise 2.3 Solutions

#### Class 10 Maths Exercise 2.3 Question 1, 2 Solutions in Videos

Class 10 Maths Exercise 2.3 Questions 1 in Video
Class 10 Maths Exercise 2.3 Questions 2 in Video

#### Class 10 Maths Exercise 2.3 Question 3, 4 Solutions in Videos

Class 10 Maths Exercise 2.3 Questions 3 in Video
Class 10 Maths Exercise 2.3 Questions 4 in Video

#### Class 10 Maths Exercise 2.3 Question 5 Solutions in Videos

Class 10 Maths Exercise 2.3 Questions 5 in Video
Class 10 Maths Exercise 2.3 All Questions in Video

#### Questions on Polynomials From Board Papers

1. What real number should be subtracted from the polynomial 3x³ + 10x² – 14x + 9, so that the polynomial 3x – 2 divides it exactly? [Answer: 5]
2. If α and β are the zeroes of the polynomial x² – 5x + m such that α – β = 1, find m. [Answer: 6]
3. If the sum of squares of zeroes of the polynomial x² – 8x + k is 40, find the value of k. [Answer: 12]
4. Write a quadratic polynomial, the sum of whose zeroes is – 3 and their product is also – 3.
5. If α and β are zeroes of the polynomial t2 – t – 4, form a quadratic polynomial whose zeroes are 1/α and 1/β. [Answer: 4t² + t – 1]

##### Important Questions on Polynomials for Board Papers
• Find the value of k such that 3x² + 2kx + x – k – 5 has the sum of zeroes as half of their product. [Answer: 1]
• If α and β are zeroes of x² – x – 2, find a polynomial whose zeroes are (2α + 1) and (2β + 1). [Answer: x² – 4x – 5]
• Find values of a and b so that x^4 + x³ + 8x² + ax + b is divisible by x² + 1. [Answer: a = 1, b = 7]
###### Questions for Practice
1. A person distributes k books to some needy students. If k is a zero of the polynomial x² – 100x – 20000, then find the number of books distributed. [Answer: 200]
2. If (k + y) is a factor of each of the polynomials y² + 2y – 15 and y³ + a, find values of k and a. [Answer: k = 3, – 5 and a = 27, – 125]
3. If x^4 + 2x³ + 8x² + 12x + 18 is divided by (x² + 5), remainder comes out to be (px + q), find values of q and q. [Answer: p = 2, q = 3]
4. –5 is one of the zeroes of 2x² + px – 15, zeroes of p(x² + x) + k are equal to each other. Find the value of k. [Answer: 7/4]
5. If two zeroes of x^4 – 6x³ – 26x² + 138 x – 35 are (2 ± √3), find other zeroes. [Answer: -5, 7]

##### How can we find the zeros of a polynomial degree n?

A polynomial p(x) of degree n, the graph of y = p(x) intersects the x-axis at atmost n points. Therefore, a polynomial p(x) of degree n has at most n zeroes.

##### What will be the factors of a polynomial if zeros are given?

If α and β are the zeroes of the quadratic polynomial p(x) = ax² + bx + c, a ≠ 0, then you know that x – α and x – β are the factors of p(x).

##### How do we pronounce the symbols α and β?

Symbols α and β are Greek letters pronounced as alpha and beta respectively.

##### What are the basic rules for polynomial division?

We first arrange the terms of the dividend and the divisor in the decreasing order
of their degrees. Arranging the terms in this order is called writing the polynomials in standard form.         