# Quadratic Equations

Quadratic Equation is an important topic in high-school curriculum. It is a vital Mathematical tool to understand various other fields of Science and Engineering especially Physics and Chemistry. Go through the following series of Lectures and Problem Solving Sessions to get a thorough grip over the subject matter.

## Contents

## Concept Lectures

Session # 1 : Introduction. What are Quadratic Equations? Why are quadratic equations called so? General form of quadratic equations.

Session # 2 : What is meant by solutions/roots of a quadratic equation? How to check if a given value is a root of a quadratic equation?

## Solved Examples

Session # 3 : Solved Example # 1 : On verifying if the given values are solutions of a given quadratic equation.

Session # 4 : Solved Example # 2 : Finding coefficients if solution to a quadratic equation is given.

## Concept Lectures

Session # 5 : Factorisation Method of solving Quadratic Equations

## Solved Examples

Session # 6 : Solved Example # 3 : Solving a Quadratic Equation using factorisation method

Session # 7 : Solved Example # 4 : Solving a Quadratic Equation using factorisation method

Session # 8 : Solved Example # 5 : Solving a Quadratic Equation using factorisation method

Session # 9 : Solved Example # 6 : Solving a Quadratic Equation using factorisation method

Session # 10 : Solved Example # 7 : Solving a Quadratic Equation using factorisation method

## Concept Lectures

Session # 11 : Solving Quadratic Equations by Completing the Square Method

## Solved Examples

Session # 12 : Solved Example # 8 : Solving a Quadratic Equation using Completing the Square Method

## Concept Lectures

Session # 13 : Shridharacharya's Method of solving Quadratic Equation

## Solved Examples

Session # 14 : Solved Example # 9 : Solving a Quadratic Equation using Sridharacharya's Method

Session # 15 : Solved Example # 10 : Solving a Quadratic Equation using Sridharacharya's Method

## Concept Lectures

Session # 16 : Nature of roots of a Quadratic Equation

## Solved Examples

Session # 17 : Solved Example # 11 : Finding the nature of roots of a quadratic equation

Session # 18 : Solved Example # 12 : Finding the nature of roots of a quadratic equation

Session # 19 : Solved Example # 13 : Problem based on the nature of roots of a quadratic equation

Session # 20 : Solved Example # 14 : Problem based on the nature of roots of a quadratic equation

Session # 21 : Solved Example # 15 : Problem based on the nature of roots of a quadratic equation

## Additional Topics

Following sessions can be utilised to gain additional knowledge in quadratic equations.

Session # 22 A Quadratic Equation can not have more than two roots

Session # 23 Relation between Sum and Product of roots and coefficients of a quadratic equation.

Session # 24 Solved Example: # 16 Relation between Sum and Product of roots and coefficients of a quadratic equation.

Session # 25 Condition for a Quadratic Equation to have roots (A) Equal in magnitude and opposite in sign & (B) Reciprocal to each other

Session # 26 Relation between the signs of the value of a quadratic polynomial and the sign of the coefficient of x^2

Session # 27 Proof of : Relation between the signs of the value of a quadratic polynomial and the sign of the coefficient of x^2

## Solved Examples

Session # 28 Solved Example: # 17 Solving equations which are not in quadratic form by converting them into a quadratic equation.

Session # 29 Solved Example: # 18 Solving equations which are not in quadratic form by converting them into a quadratic equation.

Session # 30 Solved Example: # 19 Solving equations which are not in quadratic form by converting them into a quadratic equation.

Session # 31 Solved Example: # 20 Solving equations which are not in quadratic form by converting them into a quadratic equation.

Session # 32 How to find out the value of infinitely extending nested radicals by using a quadratic equation.