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Topic 3: Quadratic Equations - Mathematics Notes Form Two
Solving Equations
- by Factorization
- by completing the square
- by using quadratic formula
The Solution of a Quadratic Equation by Factorization
Determine the solution of a quadratic equation by factorization
Example 1
Therefore, since the values of x are identical then x = -1.
Two numbers whose product is -10 and their sum is -3 are 2 and -5.
Therefore, either 2y – 1 = 0 or 5y + 1 = 0
Example 3
Therefore
Example 4
Therefore x = 4 or x = -4
The Solution of a Quadratic Equation by Completing the Square
Find the solution of a quadratic equation by completing the square
Completing the square.
Example 7
General Solution of Quadratic Equations
The Quadratic Formula
Derive the quadratic formula
The special quadratic formula used for solving quadratic equation is:
Example 8
solve 5x2 – 8x + 3 = 0 by using quadratic formula.
Given a word problem; the following steps are to be used to recognize the type of equation.
Example 11
A piece of wire 40cm long is cut into two parts and each part is then bent into a square. If the sum of the areas of these squares is 68 square centimeters, find the lengths of the two pieces of wire.
- -6x2+ 23x – 20 = 0
- X2– x -12 = 0