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WEEK 5:
TOPIC: Quadratic Equations
Content:
- Revision of factorization of perfect squares
- Making quadratic expression perfect squares by adding a constant K.
- Solution of quadratic equation by the method of completing the square
- Deducing the quadratic formula from completing the square.
- Construction of quadratic equation from sum and product of roots.
- Word problems leading to quadratic equations.
Revision of factorization of perfect squares
A quadratic expression is a perfect square if it can be expressed as the product of two linear factors that are identical. For example, x2+4x+4=(x+2)(x+2) ,x2+6x+9=(x+3)(x+3) are perfect squares.
Example 1: Factorize 😡2-22x+121
The expression is a perfect square if the first term and the constant terms are both perfect squares. The sign of the middle term of the quadratic expression can be put between the terms of the linear factors.
For x2-22x+121, the first term is the square of x and the constant term is 121 which is the square of 11.
x2-22x+121=(x-11)(x-11) =(x-11) 2
Notice that the middle term is twice the product of the terms of the linear factor. In this case, -22x=2(x)(-11)
Example 2: Factorize 400+120t+9t2
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