Free download NCERT Solutions for class 10 Maths Chapter 4 Quadratic Equations exercise 4.4, 4.3, 4.2 and 4.1 in Hindi & English medium pdf form. Solutions are as per Latest CBSE syllabus for class 10 2018-2019 MP Board, UP board & CBSE Board exams. Previously it the examination pattern was divided into SA-1 and SA-2, but now the complete syllabus will be tested in the final exam. It is very essential to learn quadratic equations, because it have wide applications in other branches of mathematics, physics, in other subjects and also in real life situations. Buy NCERT books or download NCERT books, revision books and solutions from the following links.

## NCERT Solutions for class 10 Maths Chapter 4

### Class 10 Maths Chapter 4 Solutions – English & Hindi Medium

- Class 10 Maths Chapter 4 Exercise 4.1 Solutions
- Class 10 Maths Chapter 4 Exercise 4.2Solutions
- Class 10 Maths Chapter 4 Exercise 4.3 Solutions
- Class 10 Maths Chapter 4 Exercise 4.4 Solutions
**NCERT Books in Hindi & English Medium****NCERT Exemplar Books**

A polynomial of degree two is called a quadratic polynomial. When a quadratic polynomial is equated to zero, it is called a quadratic equation. A quadratic equation of the form ax^2 bx + c = 0, a > 0, where a, b, c are constants and x is a variable is called a quadratic equation in the standard form.

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### Previous Years CBSE Questions

**Two marks questions**

1. Find the roots of the quadratic equation √2 x^2+7x+5√2=0. [CBSE 2017] 2. Find the value of k for which the equation x^2+k(2x+k-1)+2=0 has real and equal roots. [CBSE 2017]**Three marks questions**

1. If the equation (1+m^2 ) x^2+2mcx+c^2-a^2=0 has equal roots then show that c^2=a^2 (1+m^2 ).**Four marks questions**

1. Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. [CBSE 2017]

**Roots of Quadratic Equation**

**Roots of Quadratic Equation**

A zero of a polynomial is that real number, which when substituted for the variable makes the value of the polynomial zero. In case of a quadratic equation, the value of the variable for which LHS and RHS of the equation become equal is called a root or solution of the quadratic equation. There are three algebraic methods for finding the solution of a quadratic equation. These are (i) Factor Method (ii) Completing the square method and (iii) Using the Quadratic Formula.

*(i) Factor Method*

*(i) Factor Method*

Factorisation method is used when the quadratic equation can be factorised into two linear factors. After factorisation, the quadratic equation is expressed as the product of its two linear factors and this is equated to zero. See the following example to learn the step by step method.

**(ii) Completing the square method**

**(ii) Completing the square method**

**(iii) Using the Quadratic Formula**

**(iii) Using the Quadratic Formula**

Download assignments with answers. One marks questions assignments contains very short answers question based on logical concepts of the chapter. Two marks questions assignments contains short answers questions based on solution of equations and finding the value of k or other missing constants. Three marks questions assignments contains most of the proving statements between the coefficients of the variable. There are four marks questions contains word problems, like distance – time, age problems, perimeter – area questions, upstream – downstream, work – time etc. First four marks questions assignment includes proving questions, second assignment and third assignments contains word problems. Answers of the assignments age given in the same sheet.

*Historical Facts!*

*Historical Facts!*

The word quadratic is derived from the Latin word “Quadratum” which means “A square figure”.

Brahmagupta (an ancient Indian Mathematician)(A.D. 598-665) gave an explicit formula to solve a quadratic equation. Later Sridharacharya (A.D. 1025) derived a formula, now known as the quadratic formula, for solving a quadratic equation by the method of completing the square. An Arab mathematician Al-khwarizni(about A.D. 800) also studied quadratic equations of different types. It is believed that Babylonians were the first to solve quadratic equations. Greek mathematician Euclid developed a geometrical approach for finding lengths, which are nothing but * solutions* of quadratic equations.

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