The Quadratic Formula
x = (−b ± √(b² − 4ac)) / 2a
Common Mistakes
- Sign errors with negative b — always substitute negative coefficients in parentheses to avoid dropping a minus sign.
- Forgetting the ± produces two answers, not one.
- Dividing only part of the numerator by 2a — both the −b term and the square root term must be divided.
Frequently Asked Questions
What does the discriminant tell me before I even solve?
Positive means two real solutions, zero means exactly one repeated solution, negative means two complex (non-real) solutions — useful for predicting the answer type in advance.
Can I use the quadratic formula on any quadratic?
Yes — unlike factoring, which only works cleanly on certain quadratics, the quadratic formula solves every quadratic equation, including ones with irrational or complex solutions.
