Discriminant of a quadratic equation

The discriminant can be considered as a property of a quadratic equation. It is calculated from the quadratic equation in the general form. The discriminant value is very important in determining the nature of roots of a quadratic equation, even before calculating the roots themselves. This gives us the advantage of not having to calculate the roots of a quadratic equation, when knowing their nature is sufficient.

The nature of roots of a quadratic equation means the possible set of values that the roots can be. This tells us whether the roots are real numbers, imaginary numbers, complex numbers, or rational numbers, and so on..

Knowing the nature of roots of a quadratic equation is especially useful in graphing parabolas, and in checking the answers.

The discriminant can be calculated when the quadratic equation is in the general form:

ax^2 + bx + c = 0

In the above equation, the discriminant D is calculated by:

D = b^2 - 4ac

Example: In the equation

2x^2 + 3x + 5 = 0,

the discriminant is

D = 3^2 - 4(2)(5) = -31

The discriminant value in a quadratic is especially useful in determining the nature of the roots of a quadratic equation.

Read more about quadratic equations at The Math Blog