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
- = 0 — one repeated real root
- < 0 — two complex conjugate roots
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For ax² + bx + c = 0:
The value b² − 4ac (the discriminant) determines the nature of the roots:
This theorem links differentiation and integration:
Where F is any antiderivative of f, i.e. F′(x) = f(x). Consequences: