The Quadratic Formula
For ax² + bx + c = 0:
x = (-b ± √(b² - 4ac)) / (2a)
The value b² − 4ac (the discriminant) determines the nature of the roots:
- > 0 — two distinct real roots 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
- = 0 — one repeated real root
- < 0 — two complex conjugate roots 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