Explanation of working model of math | factorization of quadratic equation | Classes 7,8,9, and 10.

Quadratic Equation

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Introduction- By using this working model you can easily explain how we can factorize the quadratic equations. You can also show the quadratic equation is a geometrical shape. By showing different geometrical shapes students can easily learn the factorization method. Let us discuss it in detail.

Explanation- Firstly we have to explain that what is a quadratic equation?

To make a quadratic equation we need a square, rectangle, and one square having magnitude one.

If you want to know how to make it watch this video. 

Let us discuss it with some examples.

1. Example:x² + 4x + 3

Arrange the following shapes in such a way that it makes a perfect shape of square or rectangle but notice one thing after making the shape, you have to check opposite sides must be equal. 

Solution: X² + 3x + x + 3

x( x +3) + 1( x + 3)

(x + 3) (x + 1)

2. Example:2x² + 5x + 3

Solution:  2x² + 3x + 2x + 3

x( 2x + 3) + 1( 2x + 3)

(2x + 3) (x + 1)

3. Example:x² + 4x + 4

Solution:  x² + 2x + 2x + 4

x( x + 2) + 2( x + 2)

(x + 2) (x + 2)

4. Example:2x² + 6x + 4

2x² + 4x + 2x + 4

(x + 1) (2x + 4)

5. Example:3x² + 4x + 1

Solution:  3x² + 3x + x + 1

3x( x + 1) + 1( x + 1)

(x + 1) (3x + 1)

let us discuss some other cases. In these cases you have to place negative coffecient of x by flipping the rectangle shapes

6. Example:3x² - 7x + 4

Solution:  3x² - 4x - 3x + 4

x( 3x - 4) - 1( 3x - 4)

(3x - 4) (x - 1)

7. Example:2x² - 7x + 5

Solution:  2x² - 5x - 2x + 5

x( 2x - 5) - 1( 2x - 5)

(2x - 5) (x - 1)

Remarks:

1. You can easily find out all the real roots from this working model.

2. All types of quadratic equations can be proved.

3. This working model can be used by the 7th, 8th, 9th, and 10th classes.

If you have any doubt please comment in the comment box.

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