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

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,

• NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations
• NCERT Exemplar Solutions for Class 10 Maths Chapter 4 Quadratic Equations

Quadratic Polynomial

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

f(x) = ax² + bx + c, where a ≠ 0

Quadratic Equation

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.

3. Quadratic formula method

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.

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 Solutions of Cass 10 Subject Wise

• NCERT Solutions for Class 10 Maths
• NCERT Solutions for Class 10 Science

NCERT Class 10 Exemplar Solutions for Other Subjects:

• NCERT Exemplar Class 10 Maths solutions
• NCERT Exemplar Class 10 Science solutions