Study Notes
Quadratic equations are algebraic expressions that can have two different solutions. They can be solved using methods like factorisation or algebraic manipulation.
- Quadratic Equation — an equation of the form ax^2 + bx + c = 0 Example: x^2 - x - 6 = 0
- Factorisation — a method to solve quadratic equations by expressing them as a product of two binomials Example: (x-3)(x+2) = 0
- Algebraic Manipulation — a method involving rearranging and simplifying the equation to find solutions Example: 16x^2 - 9 = 0 becomes (4x+3)(4x-3) = 0
Exam Tips
Key Definitions to Remember
- Quadratic Equation: ax^2 + bx + c = 0
- Factorisation: Expressing a quadratic as a product of two binomials
Common Confusions
- Forgetting to find both solutions (positive and negative)
- Using square roots on negative numbers
Typical Exam Questions
- Solve x^2 - x - 6 = 0 by factorisation? x = 3 or x = -2
- Solve 16x^2 - 9 = 0 by algebraic manipulation? x = 3/4 or x = -3/4
- If the sum of two numbers is 27 and their product is 50, what are the numbers? x = 25, 2 or x = 2, 25
What Examiners Usually Test
- Ability to solve quadratic equations using different methods
- Understanding of when to use factorisation or algebraic manipulation