🧮 TI84Calc

Quadratic Equation Solver

Solve quadratic equations of the form ax² + bx + c = 0 with step-by-step discriminant evaluation and exact roots.

Enter Coefficients:

x² +
x +
= 0

Solution & Steps:

Press solve to calculate roots.

What is the Quadratic Formula?

A quadratic equation is a second-order polynomial equation expressed in the standard form ax² + bx + c = 0, where a, b, and c are numerical coefficients with a ≠ 0. Solving a quadratic equation involves finding the values of x (known as roots or zeros) that satisfy the algebraic equality.

The primary mathematical method to solve quadratic equations is the Quadratic Formula:
x = (-b ± √(b² - 4ac)) / (2a)

Understanding the Discriminant (Δ)

The term inside the radical Δ = b² - 4ac is called the discriminant. It dictates the nature of the roots:

  • If Δ > 0: The equation has two distinct real roots.
  • If Δ = 0: The equation has one real repeated root (double root).
  • If Δ < 0: The equation has two complex conjugate roots involving the imaginary unit i.