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NCERT Solutions for CBSE Class 10 | askIITians NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex Ex Class 10 Maths 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 � Estimated Reading Time: 40 secs. Polynomials: Exercise - (Mathematics NCERT Class 10th) Like the video? Therefore, sum of the zeroes = 0 + (� 2) = � 2 CLASS NCERT Solutions Science Maths Social Science Download NCERT Books Notes. 2 days ago�� NCERT Solutions for Class 10 Maths Chapter 1 Polynomials Ex Page 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x 2 � 2x � 8 (ii) 4s 2 � 4s + 1 (iii) 6x 2 � 3 � 7x (iv) 4u 2 + 8u (v) t .
Thus:

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A thorough practice of the solutions just once or twice will make all the difference. You can be sure of the fact that noting will be asked in the question paper outside the concepts and questions solved in the notes provided by Vedantu.

The notes are for you and Vedantu knows what you need. The highest power of the variable appearing in the polynomial is called its degree. For example,. The degree of the zero polynomial is not established. A linear polynomial is one degree of the polynomial. A polynomial that is of a degree two is called a quadratic polynomial. A polynomial that is of a degree 3 is called a cubic polynomial.

A biquadratic polynomial is a polynomial of degree 4. A real number is said to be a zero of a polynomial. Remainder theorem: To understand the remainder theorem, we must have knowledge about factors and multiples, long division algorithms. If f x is any Class 10th History Chapter 2 Ncert Solutions Ltd polynomial of a degree 1 and f x is divided by the linear polynomial x � a, then the remainder is f a. Factor theorem: Sometimes a polynomial having values that are unknown and one of its factors are provided and we have to calculate the value of that unknown value.

Sometimes, a linear polynomial is given and we have to verify whether it is a factor of given polynomial f x of degree greater than 1 or not. For solving such types of problems factor theorem is required. In this segment, we will study division algorithms for polynomials. If any two polynomials like p x and g x along with one polynomial of the two is not equal to 0 i. The outcome of the above numerical is known as the Division Algorithm for polynomials.

In other words, we can say that when p x divided by g x , we get q x as quotient and r x as remainder. Organize the terms of the dividend and the divisor in descending order of their degrees.

The first term of the dividend must be divided by the first term of the divisor to obtain the first term of the quotient. Multiply the whole divisor by the first term if the quotient and subtract the result obtained from the dividend.

Observe the remainder as the new dividend and proceed as earlier. There are a total of 4 Exercises including an optional Exercise in the 2nd chapter of class 10 Maths. The first Exercise is about to find zeros of polynomials p x. In the second Exercise, the students need to find a quadratic polynomial. The third Exercise has questions on division of polynomials.

The last Exercise covers questions from all the concepts of Class 10 Maths Chapter 2. Exercise 2. The third chapter of class 10 maths is about the linear equations in two variables.

It describes what a linear equation in two variables is and how to solve the problems on linear equations in two variables. In the first Exercise Ex 3. The second Exercise, i. The next four Exercises, Ex 3. The methods explained here are algebraic method, cross-multiplication method, elimination method and substitution method.

Exercise 3. It contains questions from all the Exercises. This chapter explains what a quadratic equation is and the methods of solving quadratic equations.

It also explains the factorization method of solving quadratic equations and the square method. The chapter gives the details of relationships between discriminant and nature of roots. Also, the problems of real life have been solved as examples in this chapter. Exercise 4.

This chapter introduces a new topic to the students - Arithmetic Progression, commonly called as AP. Students will learn what is AP, derivation of nth term, finding the sum of first n terms of the AP and solving the real life problems using AP in this chapter.

The first Exercise of the chapter teaches how to represent a problem or situation in the form of AP, how to find the first term and difference of the AP, and to find whether the given series is Ap or not.

The next Exercise, Ex 5. The third Exercise describes how to find the sum of first n terms of AP and contains questions related to the topic. The last and fourth Exercise have questions related to the topics taught in the chapter. Exercise 5. The chapter 6 of class 10 gives details about the triangles. The chapter gives details about the figures with the same shape but different sizes.

It explains the similarity of the triangles, theorems associated with the similarity of triangles and the concept of congruent triangles. Further, theorems related to areas of triangles, the Pythagoras theorem and the converse of pythagoras theorem is explained. Exercise 6. Class 10 Maths Chapter 7 explains coordinate geometry, the maths of locating a given point with the help of an ordered pair of numbers.

The coordinate or cartesian geometry helps to find the distance between two points whose coordinates are given. The concept of finding the area of a triangle formed by three given points. Also, the ways of finding the coordinates of the point which divides a line segment joining two given points in a given ratio is explained in the chapter. Exercise 7. Trigonometry is the study of the ratio of right triangles with respect to the acute angles, which are known as trigonometric ratios of the angles.

Students will also learn to calculate trigonometric ratios for the given angles and also a few trigonometric identities. Exercise 8. Chapter 9 is the continuation of chapter 8 where the students will learn about the application of trigonometry which they learnt in the previous chapter. This chapter helps to understand how trigonometry is applied to our everyday life to find out the height and distance of various objects.

They will also learn how trigonometry is applied and used in navigation, construction and determining the position of any piece of land based on their latitude and longitudes. Exercise 9. In this chapter, students will be introduced to the concept of tangents and number of tangents from a point on a circle.

Exercise Chapter 11 is one of the interesting chapters. This chapter is all about constructing various geometric figures. The students will learn to divide a line segment, and how to draw tangents to a circle. The methods of construction are well explained in the chapter to clear the concepts.

As the name suggests, the chapter is about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle is clarified here. This chapter further explains how to find the area of the figures that contains a circle or part of a circle. In the five Exercises of this chapter, finding the surface area of any object which is made up of two or more different solid shapes. The solid shapes include cuboid, cone, sphere, hemisphere and cylinder.

Then, there are questions on finding the volume of the objects that are again made up of two different solid shapes. Also, there are questions which ask about the conversion from one shape to another.

This chapter further explains how to find the volume, curved surface area and total surface area of a frustum of a cone. This is another interesting chapter where the students learn about the numerical representation of data, grouped or ungrouped. They further learn about finding the mean, median and mode of the given data.

In the next Exercise, they will learn about the cumulative frequency distribution and drawing cumulative frequency curves. It elaborates and explains the difference between experimental probability and theoretical probability.

The chapter is full of Class 10th Ncert 2.2 Cell examples to clear the concept of probability to the learners. Students can download the PDF easily and start going through the chapters. You will find clear categorisation and step by step solutions of all the questions with a clear conclusion. This will help you to understand how you can write answers in your exams to help you score well. The exam is of marks where 80 marks is for theory whereas 20 marks is given for internal assessment.

To understand the marking scheme in a better way, you should understand the exam pattern clearly.

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