Quadratic Equations

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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Concept Map

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Textbook

Please click here for Karnataka and other text books.

1. Karnataka text book for Class 10, Chapter 09 - Quadratic Equations
2. cbse text book

Additional Information

Useful websites

For more information about quadratic equation

Reference Books

relevent references

Teaching Outlines

Concept #1 - Introduction to quadratic equations

An equation of the form $ax^{2}+bx+c=0$ where a ≠ 0 and a, b, c belongs to R.

Learning objectives

converting verbal statement into equations.

Notes for teachers

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

Activities

1. Activity No 1 Introduction to quadratic equation
2. Activity No 2 Making a rectangular garden
3. Activity No 3 Understanding$ax^{2}+bx+c=0$ geometrically

Concept #2 - Types of equations

Pure Quadratic Equation & Adfected Quadratic Equation

Quadratic equation,in the form $ax^{2}+bx+c=0$, is termed as quadratic expression and the equation of the form $ax^{2}+bx+c=0$, 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

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

Notes for teachers

1. Knowledge of general form of quadratic equations
   
2. roots of equation
   
3. proper use of signs.

Activities

Identifying pure and adfected ouadratic equations- Activity No1

work sheet Activity No2

Concept #3 What is the solution of a quadratic equation

The roots of the Quadratic Equation which satisfy the equation

Learning objectives

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

Notes for teachers

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

Activities

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

Concept #4Methods of solution

Different methods of finding the solution to a quadratic equation

1. Factorisation method
2. Completing the square method
3. Formula method
4. Graphical method.

Learning objectives

1. Solving quadratic equation by factorisation method
2. Solving quadratic equation by completing the square method
3. Deriving formula to find the roots of quadratic equation.
4. Solving quadratic equation by using formula.
   
5. Solving quadratic equation graphically.
   
6. 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

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

Concept #5Nature 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

1. 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

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

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

Concept #6applications

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

1. Activity No #1 more word problems
2. 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 $2a^{2}-4a+1=0$ find the value of $p^{3}+q^{3}$
solution
2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.
solution
3.Solve $x^{2}-4x-8=0$ By completing the square.
solution