Online calculator. Quadratic equation solver.

is a polynomial equation of the second degree. The general form is

a x² + b x + c = 0,

where represents a variable or an unknown, and , , and are constants with ≠ 0. (If = 0, the equation is a linear equation.)

To solve a quadratic equation means to find all values x_i, at which we have the equality

a x_i² + b x_i + c = 0.

Quadratic Formula.

Expression (∆ = b² - 4 a c) is called the discriminant.

• If the discriminant is positive (∆ > 0), then there are two distinct roots, both of which are real numbers.
• If the discriminant is zero (∆ = 0), then there is exactly one distinct real root, sometimes called a double root (
  x
  ₁ = 
  x
  ₂).
• If the discriminant is negative (∆ < 0), then there are no real roots.