A quadratic equation is a second-degree polynomial equation in one variable \(x\), generally expressed as:
\[ ax^2 + bx + c = 0, \quad a \neq 0 \]
Standard Form:
\[ ax^2 + bx + c = 0 \]
Quadratic Formula (Solutions):
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Discriminant:
\[ \Delta = b^2 - 4ac \]
The discriminant determines the nature of roots:
Sum and Product of Roots:
\[ \text{Sum} = \alpha + \beta = -\frac{b}{a}, \quad \text{Product} = \alpha \beta = \frac{c}{a} \]
