Quadratic Equations Class 10th Notes - Free NCERT Class 10 Maths Chapter 4 Notes - Download PDF

# Quadratic Equations Class 10th Notes - Free NCERT Class 10 Maths Chapter 4 Notes - Download PDF

Edited By Safeer PP | Updated on Mar 19, 2022 10:36 AM IST

Quadratic equations are the NCERT chapter which deals with algebraic equations of degree 2. The NCERT Class 10 Maths chapter 4 notes covers a brief outline of the chapter quadratic equations. The main topics covered quadratic equations Class 10 notes, gives you properties and roots of quadratic equations. Class 10 Maths chapter 4 notes also cover the basic equations in the chapter. Quadratic equations Class 10 notes pdf download contains all of these topics.

Also, students can refer,

A polynomial with degree 2, is a quadratic polynomial. It is in the form of

f(x) = ax2 + bx + c, where a ≠ 0

An algebraic expression of the second degree is called a quadratic equation.

• The standard form of a Quadratic Equation

ax2+bx+c=0

where a, b and c are the real numbers and a≠0

## Roots of a Quadratic Equation

Let x = α and α is a real number. If α satisfies the quadratic equation ax2+ bx + c = 0 such that aα2 + bα + c = 0, then α is the root of the Quadratic Equation.

As quadratic polynomials have degree two, therefore quadratic equations can have two roots. Thus, the zeros of a quadratic polynomial f(x) =ax2+bx+c is same as the roots of the quadratic equation ax2+ bx + c= 0.

## Methods to Solve the Quadratic Equations

Three methods to solve the Quadratic Equations-

### 1. Factorization Method

In this method, divide the equation into two linear factors and equate each factor to zero to find the roots of the equation.

Step 1: Quadratic Equation in the form of ax2 + bx + c = 0.

Step 3: By factorization, we write ax2 + bx + c = 0 as (x + p) (x + q) = 0

For example-

x2-2x-15=0

(x+3)(x-5)=0

x+3=0 or x-5=0

x=-3 or x=5

x={-3,5}

The above values of x are the two roots of the given quadratic equation.

### 2. Completing the Square Method

In this method, convert the equation in the square form (x + a)2 - b2= 0 to find the roots.

Step1: Quadratic Equation in the standard form ax2 + bx + c = 0.

Step 2: Divide both the sides by a:

Step 3: Transfer the constant to RHS then add the square of the half of the coefficient of x i.e. (b/2a)2 on both the sides

Step 4: Write LHS as a perfect square and simplify RHS.

Step 5: Square root on both sides.

Step 6: Constant terms are shifted to the RHS and calculate the value of x as there is no variable at the RHS.

In this method, find the roots by using the quadratic formula. The quadratic formula is

where a, b and c are the real numbers and b2 – 4ac is known as a discriminant.

## Nature of Roots

The nature of the roots of the equation depends upon the value of D, which is called the discriminant.

 Value of discriminant Number of roots D>0 Two distinct real roots D=0 Two equal and real roots D<0 No real roots

## Significance of NCERT Class 10 Maths Chapter 4 Notes-

Quadratic Equations Class 10 notes will help to understand the formulas, statements, rules in detail.

This NCERT Class 10 Maths chapter 4 notes also contains previous year’s questions and NCERT TextBook pdf. It also contains FAQs or frequently asked questions along with topic-wise explanations.

In offline mode, Class 10 Maths chapter notes pdf download can be used to prepare.

## Class 10 Chapter Wise Notes

 NCERT Class 10 Maths Chapter 1 Notes NCERT Class 10 Maths Chapter 2 Notes NCERT Class 10 Maths Chapter 3 Notes NCERT Class 10 Maths Chapter 4 Notes NCERT Class 10 Maths Chapter 5 Notes NCERT Class 10 Maths Chapter 6 Notes NCERT Class 10 Maths Chapter 7 Notes NCERT Class 10 Maths Chapter 8 Notes NCERT Class 10 Maths Chapter 9 Notes NCERT Class 10 Maths Chapter 10 Notes NCERT Class 10 Maths Chapter 11 Notes NCERT Class 10 Maths Chapter 12 Notes NCERT Class 10 Maths Chapter 13 Notes NCERT Class 10 Maths Chapter 14 Notes NCERT Class 10 Maths Chapter 15 Notes

## NCERT Class 10 Exemplar Solutions for Other Subjects:

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1. What is factorization according to Class 10 Math’s chapter 4 notes?

The process by which the bracket of a quadratic equation is reduced is called factorization.

2. What is the weightage of Class 10 Quadratic Equations notes in the board examination?

Students can expect 4 to 8 marks questions from the notes for Class 10 Math’s chapter 4.

3. How many methods are there to find the roots of a quadratic equation?

In the notes for Class 10 Math’s chapter 4, four methods are discussed to find the roots of a quadratic equation.

4. How does this chapter help students?

It is evident that this chapter gives a better understanding of quadratic polynomials and helps us understand quadratic equations in a more wholesome way. Students can use Class 10 Math’s chapter 4 notes pdf download for revision

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