# NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.4

NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.4 Polynomials (10 Maths Ex. 2.4) or Bahupad in Hindi Medium and English Medium study online or download in PDF updated for session 2020-21 based on latest NCERT Books. Download contents for offline use in PDF file format. These Mathematics solutions are useful for all the board who are using CBSE NCERT Books for their exams. For example, UP Board High School students are now using NCERT Textbooks, so they can download UP Board Solutions for 10 Maths Exercise 2.4 from here in Hindi or English Medium. All the content on Tiwari Academy is free to use.

No login or registration is required to access any content. Class 10 Maths Solutions for CBSE Board, Gujrat board, Uttarakhand Board, MP Board and UP Board are updated for students following the NCERT Books for the academic session 2020-21 onward. Download (Exercise 2.4) in PDF or use online without downloading.

## NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.4

 Class: 10 Maths (English and Hindi Medium) Chapter 2: Exercise 2.4

### 10 Maths Chapter 2 Exercise 2.4 Solutions

NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.4 Polynomials in English and Hindi Medium for online use as well as offline in PDF form free download for 2020-21. If you want to download, the link is given on this page. Move to Class 10 Maths Chapter 2 main page to download all the exercises in PDF. UP Board students can use the same NCERT Solutions for Class 10 Maths.

• ### Class 10 Maths Exercise 2.4 Solutions

#### Class 10 Maths Exercise 2.4 Question 1 Solutions in Video

Class 10 Maths Exercise 2.4 Question 1 (I) in Video
Class 10 Maths Exercise 2.4 Question 1 (II) in Video

#### Class 10 Maths Exercise 2.4 Question 2, 3 Solutions in Video

Class 10 Maths Exercise 2.4 Question 2 Solutions in Video
Class 10 Maths Exercise 2.4 Question 3 Solutions in Video

#### Class 10 Maths Exercise 2.4 Question 4, 5 Solutions in Video

Class 10 Maths Exercise 2.4 Question 4 Solutions in Video
Class 10 Maths Exercise 2.4 Question 5 Solutions in Video

#### Important Questions on Polynomials

• Sum and product of two zeroes of x^4 – 4x³ – 8x² + 36x – 9 are 0 and – 9 respectively. Find the sum and product of its other two zeroes. [Answer: 4, 1]
• Obtain zeroes of 4√3x²+5x – 2√3 and verify relation between its zeroes and coefficients. [Answer: -2/√3, √3/4]
• What must be subtracted from 8x^4 + 14x³ – 2x² + 7x – 8 so that the resulting polynomial is exactly divisible by 4x² + 3x – 2? [Answer: 14x – 10]
• Find all zeroes of the polynomial 2x³ + x² – 6x – 3 if two of its zeroes are 3 and – 3. [Answer: √3, -√3, – 1/2]
• If √2 is a zero of (6x³ + √2x² –10x – 4√2), find its other zeroes. [Answer: -√2/2, -2√2/3]
##### Questions for Practice
1. On dividing the polynomial x³ – 5x² + 6x – 4 by a polynomial g(x), quotient and remainder are (x –3) and (– 3x + 5) respectively. Find g(x). [Answer: x² – 2x + 3]
2. What must be added to 4x^4 + 2x³ – 2x² + x – 1 so that the resulting polynomial is divisible by x² – 2x – 3? [Answer: 61x – 65]
3. If sum and product of two zeroes of the polynomial x³ + x² – 3x – 3 are 0 and 3 respectively, find all zeroes of the polynomial. [Answer: √3, -√3, -1]
4. If -1/2 is a zero of the polynomial 2x³ + x² – 6x – 3, find the sum and product of its other two zeroes. [Answer: 0, 3]
5. If α and β are zeroes of y² + 5y + m, find the value of m such that (α + β)² –αβ = 24. [Answer: 1]
###### Questions from Board Papers
• Obtain all zeroes of the polynomial 2x^4 – 2x³ – 7x² + 3x + 6 if two factors of this polynomial are (x ± √3/2). [Answer: 2, -1, ±√3/2]
• One zero of x³ – 12x² + 47x – 60 is 3 and the remaining two zeroes are the number of trees planted by two students. Find the total number of trees planted by both students. [Answer: 9]

##### How do we start division of a polynomial by another polynomial?

To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor. Then carry out the division process.

##### What are the division algorithm for Polymomials?

If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x). This result is known as the Division Algorithm for polynomials.

##### What are the linear, quadratic and cubic polynomials?

Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.

##### What are the number of zeros for a quadratic or cubic polynomial?

A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.         