Quadratic Equations Standard Form and Discriminant

Quadratic Equations

• The standard form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $a ≠ 0$.

Discriminant of a Quadratic Equation

• The discriminant of a quadratic equation is represented by the symbol Δ (delta) and is calculated using the formula: Δ = $b^2 - 4ac$.
• The discriminant is used to determine the number and nature of the roots of a quadratic equation.

Sum of Roots of a Quadratic Equation

• The sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is equal to $-\frac{b}{a}$.

Interpretation of the Discriminant

• The value of the discriminant indicates the nature of the roots of a quadratic equation:
  • If Δ > 0, the equation has two distinct real roots.
  • If Δ = 0, the equation has one repeated real root.
  • If Δ < 0, the equation has no real roots (i.e., it has complex roots).