The big picture
One number, b² − 4ac, counts the real roots. The other lessons find them.
| Idea | Remember | Example |
|---|---|---|
| The form | Tidy to ax² + bx + c = 0, with a ≠ 0. | x² + 2x = x² + 5 is linear |
| The root | A value that balances both sides. | x = 4 is a root of x² − 4x = 0 |
| Split and solve | Split the middle, bracket, set each to 0. | 2x² − 7x + 3 = 0 → 1/2, 3 |
| The formula | x = (−b ± √(b² − 4ac)) / 2a. | x² − 2x − 3 = 0 → 3, −1 |
| The decider | b² − 4ac: above zero two roots, zero one, below zero none. | x² + x + 1 = 0 → none |
| Two kinds | Decider above zero: a perfect square gives rational roots. Any other gives irrational roots, still real. | x² − 4x − 1 = 0 → 2 ± √5 |
| Picking a method | Perfect square, 0 too: factorise. Above zero, not a square: formula. | below zero → say so |
| Stories | Name it, build it, solve it, keep the root the world allows. | orchard → 5 m, not −8 |
Chapter 4 of your Mathematics book is Quadratic Equations. You can count its real roots before you find one. Now open the chapter and try its exercises.