Worked example
x² − 5x + 6 = 0
- Factoring gives (x − 2)(x − 3) = 0.
- The formula uses Δ = 1 and gives (5 ± 1)/2.
- Both methods return x = 2 or x = 3.
- Substitution checks the shared result.
Math guide
Use the shortest method that stays reliable.
Choose between factoring and the quadratic formula based on the coefficients, required explanation and reliability.
Factoring is fast when integer or simple rational factors are visible. The quadratic formula works for every quadratic with a nonzero leading coefficient and makes the discriminant explicit. Both methods should produce the same complete root set.
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