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

• ### Class 10 Maths Exercise 4.1 Solutions

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

### 10 Maths Chapter 4 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.

### What is the standard form of quadratic equation in 10th Maths Ex. 4.1?

A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers, a ≠ 0. For example, 2x² + x – 300 = 0 is a quadratic equation. Similarly, 2x² – 3x + 1 = 0, 4x – 3x² + 2 = 0 and 1 – x² + 300 = 0 are also quadratic equations. In fact, any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. When we write the terms of p(x) in descending order of their degrees, then we get the standard form of the quadratic equation. That is, ax² + bx + c = 0, a ≠ 0 is called the standard form of a quadratic equation.

### What type of questions students will solve in exercise 4.1 of 10th Maths?

There are 2 questions in exercise 4.1 (chapter 4 Quadratic equations) of class 10 mathematics. In first question students have to check whether the given equation is quadratic or not.
Example of first question:
Check whether the following are quadratic equations:
(x – 2)(x + 1) = (x – 1)(x + 3) (ii) (x – 3)(2x +1) = x(x + 5)

In second question students have to represent the given situation in the form of quadratic equation.
Example of situation: A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

### Which question of exercise 4.1 class 10th Maths are easy to solve?

Students can easily do Q1 of exercise 4.1 (chapter 4 Quadratic equations) of class 10th mathematics.

### Which question of exercise 4.1 of class 10th Maths, students find difficult and why?

Students find Q2 of exercise 4.1 (chapter 4 Quadratic equations) of class 10th mathematics difficult because Q2 contains 4 word problems and generally students think word problems are difficult to solve.      