Some quadratics factor nicely. Most don't. That's why the quadratic formula exists — and why it's worth memorising forever.
There is a lot of jargon around this one. Strip it away and the math is genuinely simple. Some quadratics factor nicely. Most don't. That's why the quadratic formula exists — and why it's worth memorising forever.
For ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) / 2a.
b² − 4ac. Positive → 2 real roots. Zero → 1 double root. Negative → 2 complex roots.
When you can spot two numbers that multiply to ac and add to b. Otherwise, formula.
Projectile motion, area optimisation, business profit modelling, AC circuit calculations.
Why ±? Square roots have two solutions. Both must be considered.
What if a = 0? It's not a quadratic — it's linear. Use bx + c = 0 → x = −c/b.
Run your own numbers before you trust a rule of thumb. Two minutes saves a lot of regret.