# NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.1

NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1 (Class 10 Ex. 4.1) Quadratic Equations View in Video Format with Hindi Medium and English Medium. You can download these CBSE NCERT Solutions in PDF format for academic session 2020-21. Uttar Pradesh Madhyamik Shiksha Parishad, Prayagraj also implemented NCERT Books as a course books for academic session 2020-2021. So UP Board High School students can take benefits of these solutions free of cost. Download UP Board Solution for Class 10 Maths Exercise 4.1 in Hindi Medium. All the solutions are applicable for CBSE Board as well as UP Board and Uttarakhand Board students who are using NCERT Books for 2020-2021.

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## NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1

 Class: 10 Maths (English and Hindi Medium) Chapter 4: Exercise 4.1

• ### Class 10 Maths Exercise 4.1 Solutions

#### Class 10 Maths Chapter 4 Exercise 4.1 Solution in Videos

Class 10 Maths Exercise 4.1 Solution in Hindi
Class 10 Maths Chapter 4 Exercise 4.1 Solution

#### Important Terms Related to Quadratic Equations

1. Quadratic Equation: An equation of the form ax² + bx + c = 0, a ≠ 0 is called a quadratic equation in one variable x, where a, b and c are constants. For example 2 x² – 3x + 1 = 0
2. Roots of a Quadratic Equation: Let ax² + bx + c = 0, be a quadratic equation. If α is a root of this equation. It means x = α satisfies this equation i.e., aα² + bα+ c = 0.
3. Discriminant: For the quadratic equation ax² + bx + c = 0 the expression is called the discriminant and denoted by D. Then the roots of the quadratic equation are given by (–b ± √D)/2a.

##### Points to be Remembered
• Number of Roots: A quadratic equation has two roots, one roots or no roots, it is depending the value of D.
1. If D > 0, it has two distinct real roots.
2. If D = 0, it has two equal roots.
3. If D < 0, there is no real roots.
• Methods for Solving Quadratic Equation
1. By factorization
2. By completing the square
• Quadratic Formula to find roots of ax² + bx + c = 0 is given by x = (– b – √D)/2a and x = (– b + √D)/2a.

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##### Check whether the following are quadratic equations: (x – 2)² + 1 = 2x – 3

LHS = (x – 2)2 + 1 = x2 – 4x + 4 + 1 = x2 – 4x + 5
Therefore, (x – 2)² + 1 = 2x – 3 can be rewritten as
x² – 4x + 5 = 2x – 3
i.e., x² – 6x + 8 = 0
It is of the form ax² + bx + c = 0.
Therefore, the given equation is a quadratic equation.

##### What is the relation between zeros of a quadratic polynomial and roots of a quadratic equation?

The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same.

##### How can we check an equation is whether quadratic or not?

After the simplification, write the equation in standard format. If the maximum power of the variable is 2 and all powers are in whole numbers, the equation is quadratic equation.

##### What is discriminant in a quadratic equation?

b² – 4ac determines whether the quadratic equation ax² + bx + c = 0 has real roots or not, b² – 4ac is called the discriminant of this quadratic equation.      