# Quadratic Equations

Philosophy of Mathematics |

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## Concept Map

## Textbook

Please click here for Karnataka and other text books.

## Additional Information

### Useful websites

For more information about quadratic equation

### Reference Books

### Resources

#### Resource Title

#### Description

This interactive activity helps you realize the action of the three coefficients a, b, c in a quadratic equation.

## Teaching Outlines

## Concept #1 - Introduction to quadratic equations

An equation of the form where a ≠ 0 and a, b, c belongs to R.

### Learning objectives

converting verbal statement into equations.

### Notes for teachers

- Basic knowledge of equations, linear equations,general form of linear equation, finding the rooots of equation, graphical representation of linear equations.
- More importance to be given for signs while transforming the equations.

### Activities

- Activity No 1
**Introduction to quadratic equation** - Activity No 2
**Making a rectangular garden** - Activity No 3
**Understanding geometrically**

## Concept #2 - Types of equations

### Pure Quadratic Equation & Adfected Quadratic Equation

Quadratic equation,in the form , is termed as quadratic expression and the equation of the form , a≠0 is called quadratic equation in x. This equation is also known to be pure quadratic equation if the value of b is zero i.e. b=0. Otherwise it is said to be adfected. The letters a, b, and c are called coefficients: and c is the constant coefficient.

### Learning objectives

- To distinguish between pure & adfected equations among the given equations.
- Standard forms of pure & adfected quadratic equations.

### Notes for teachers

- Knowledge of general form of quadratic equations
- roots of equation
- proper use of signs.

### Activities

**Identifying pure and adfected ouadratic equations- Activity No1**

## Concept #3 What is the solution of a quadratic equation

The roots of the Quadratic Equation which satisfy the equation

### Learning objectives

- x=k is a solution of the quadratic equation if k satisfies the quadratic equation
- Any quadratic equation has at most two roots.
- The roots form the solution set of quadratic equation.

### Notes for teachers

- different methods of solving quadratic equation
- knowledge of suitable formula to be used to solve specific problem.
- identify the type of quadratic equation.

### Activities

- Activity No #1 #Activity No 3-quadratic formula
- Activity No #2
**Concept Name - Activity No**

## Concept #4Methods of solution

Different methods of finding the solution to a quadratic equation

- Factorisation method
- Completing the square method
- Formula method
- Graphical method.

### Learning objectives

- Solving quadratic equation by factorisation method
- Solving quadratic equation by completing the square method
- Deriving formula to find the roots of quadratic equation.
- Solving quadratic equation by using formula.
- Solving quadratic equation graphically.
- To find the sum and product of the roots of the quadratic equations.

### Notes for teachers

- Students need to know factorisation
- substitution of values and simplification
- Identifying suitable method

### Activities

- Activity No 1 -geogebra
- Activity No 2-learn more how to solve Q.E
- Activity 3-learn quadratics
- Activity 4- Quadratic Equation solution

## Concept #5**Nature of roots**

The roots of a quadratic equation can be real & equal, real & distinct or imaginary. Nature of roots depends on the values of b^-4ac.

### Learning objectives

- To find the discriminant & interpret the nature of the roots of the given quadratic equation.

### Notes for teachers

Guiding in Identifying the nature based on the value of discriminant

### Activities

- Activity No #1
**Concept Name - Activity No.**the nature of roots/ interpret the nature of the roots

- Activity No #2
**Concept Name - Activity No.**

## Concept #6**applications**

Solving problems based on quadratic equations.

### Learning objectives

By applying the methods of solving quadratic equations, finding the solutions to real life situations.

### Notes for teachers

Help the students in Identifying parameters and suitable methods for solving application problems.

### Activities

- Activity No #1 more word problems
- Activity 2:quadratics in real life

# Assessment activities for CCE

.quiz

# Hints for difficult problems

1.If P & q are the roots of the equation find the value of

solution

2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.

solution

3.Solve By completing the square.

solution