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).

Test your knowledge of quadratic equations by answering questions about the standard form, discriminant, and the sum of roots. Understand the significance of the discriminant in relation to the roots of a quadratic equation.