Why is b2 -4ac called the discriminant?

Answer 1

For a quadratic equation of the form y = ax^2 + bx + c where a, b and c are real and a is non-zero, b^2 - 4ac enables you to distinguish between the following three possible outcomes:

• b^2 - 4ac > 0 => the equation has two real roots which are different,
• b^2 - 4ac = 0 => the equation has two real root which are coincident,
• b^2 - 4ac < 0 => the equation has two roots which form a complex conjugate pair.