What Is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree 2. The standard form is:
ax² + bx + c = 0, where a ≠ 0
Methods of Solving Quadratic Equations
1. Factorisation
Example: x² + 5x + 6 = 0
Find two numbers that multiply to 6 and add to 5: they are 2 and 3
(x + 2)(x + 3) = 0
x = −2 or x = −3
2. Completing the Square
x² + 6x + 5 = 0
x² + 6x = −5
x² + 6x + 9 = −5 + 9 = 4
(x + 3)² = 4
x + 3 = ±2
x = −1 or x = −5
3. Quadratic Formula
x = [−b ± √(b² − 4ac)] / 2a
The discriminant (b² − 4ac) tells us about roots:
- b² − 4ac > 0 → two distinct real roots
- b² − 4ac = 0 → one repeated real root
- b² − 4ac < 0 → no real roots (complex roots)