Quadratic Equation & Roots

1. Quadratic Equation: \( ax^2 + bx + c = 0 \)
2. Roots: \( \alpha = \frac{-b + \sqrt{b^2 - 4ac}}{2a} \), \( \beta = \frac{-b - \sqrt{b^2 - 4ac}}{2a} \)
3. Sum of roots: \( \alpha + \beta = -\frac{b}{a} \)
4. Difference of roots: \( \alpha - \beta = \frac{\sqrt{b^2 - 4ac}}{a} \)
5. Product of roots: \( \alpha \cdot \beta = \frac{c}{a} \)