 NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.4 of Polynomials in Hindi and English medium for State board and other boards. Ace your Class 10 Maths exams with our expert NCERT Solutions for Chapter 2 Exercise 2.4 on Polynomials. Offered in both Hindi and English Medium, our guide is tailor-made for State Board, UP Board, MP Board, and other board students. Master Polynomials and excel in your studies today!

• ## Class 10 Maths Exercise 2.4 Solutions

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

 Class: 10 Mathematics Chapter 2: Exercise 2.4 Medium: English and Hindi Medium Content: NCERT Solutions

### 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. 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.

#### Important Questions on Polynomials

• Sum and product of two zeroes of x⁴ – 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 8x⁴ + 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 4x⁴ + 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 2x⁴ – 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.

### How many questions are there in exercise 2.4 of class 10th mathematics?

Exercise 2.4 of class 10th mathematics chapter 2 (Polynomials) is an optional exercise. There are in all 5 questions in exercise 2.4 of class 10th mathematics chapter 2 (Polynomials) and all questions are of different type.

### Do the questions ask from exercise 2.4 of 10th mathematics in Board exams?

Yes, questions can come from exercise 2.4 (chapter 2 Polynomials) of class 10th mathematics in Board exams.

### Which are the most important questions in exercise 2.4 of class 10th mathematics?

Q2, 3, 4 and 5 are important questions of exercise 2.4 of class 10th mathematics chapter 2 (Polynomials).

### Is exercise 2.4 of class 10th Maths easy?

Exercise 2.4 (chapter 2 Polynomials) of class 10th mathematics is difficult and logical. But difficulty level of anything varies from student to student. So, Exercise 2.4 (chapter 2 Polynomials) of class 10th mathematics is easy or not depends on students also. Some students find it difficult some find it easy or some find it in middle of easy and difficult.         Last Edited: November 1, 2023