b^2 – 4ac – The discriminant of the quadratic equation

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Quadratic equations are nothing more than second degree polynomials and, usually, they come in the form of y = ax² + bx + c.

There are many methods to solve second degree polynomial equations but, the most used one is the application of the Bhaskara formula, also known as the quadratic formula:

The discriminant of the quadratic equation is the part that is below the square root of the quadratic formula. In some books, the discriminant is represented by the greek letter Δ (delta), and Δ = b2 – 4ac. The discriminant can be positive, negative or equal to 0 (zero) such as:

  • if b2-4ac > 0, the equation has two distinct real solutions (x1 ≠ x2);
  • if b2-4ac = 0, the equation has only one real solution (x1 = x2);
  • if b2-4ac < 0, the equation has no real solutions;