Introduction
Quadratic equations are one of the most tested topics in WAEC and JAMB Mathematics. If you can master them, you're already ahead of 60% of candidates. In this guide, we'll cover all three main methods with clear examples.
What Is a Quadratic Equation?
A quadratic equation is any equation of the form ax² + bx + c = 0, where a ≠ 0. The highest power of the variable is 2, which is what makes it "quadratic" (from the Latin for square).
Method 1: Factorization
This is the fastest method when it works. The goal is to rewrite the equation as a product of two brackets.
Example: Solve x² + 5x + 6 = 0
Find two numbers that multiply to give 6 and add to give 5. Those numbers are 2 and 3.
So: (x + 2)(x + 3) = 0
Therefore: x = -2 or x = -3
Method 2: Completing the Square
This method works for all quadratics and is essential when factorization fails.
Example: Solve x² + 6x + 5 = 0
- Move constant: x² + 6x = -5
- Add (b/2)² to both sides: x² + 6x + 9 = -5 + 9 = 4
- Factor left side: (x + 3)² = 4
- Square root both sides: x + 3 = ±2
- Therefore: x = -1 or x = -5
Method 3: The Quadratic Formula
The most powerful method — it works for every quadratic equation. The formula is:
x = (-b ± √(b² - 4ac)) / 2a
Example: Solve 2x² - 4x - 6 = 0
Here a=2, b=-4, c=-6
x = (4 ± √(16 + 48)) / 4 = (4 ± √64) / 4 = (4 ± 8) / 4
x = 3 or x = -1
WAEC/JAMB Tips
- Always check your answers by substituting back into the original equation
- The discriminant (b² - 4ac) tells you the nature of roots — know this for theory questions
- Practice at least 20 past questions on quadratics before your exam
- Download our free WAEC Mathematics Past Questions below!
Conclusion
With consistent practice, quadratic equations become second nature. Start with factorization, move to completing the square, and always have the quadratic formula as your backup. You've got this!