# Discriminant meaning in math explained

Learn and know the meaning of discriminant in math. The word discriminant comes in quadratic equations chapter. Based on discriminant, we define nature of roots of a quadratic equations. So it is very much needed to know the discriminant meaning.

We all know that for finding the roots of quadratic equations there are two methods. First method is splitting the middle term and second method is by using the formula. In the formula we call “b2 – 4ac” as the discriminant. Discriminant is represented by the symbol Δ. The symbol we pronounce as Delta. The meaning of this discriminant is it tells us that what kind of roots (whether the roots are rational or irrational or equal or complex) we get for a quadratic equations.

## Roots of quadratic equation based on discriminant values:

If the discriminant i.e. b2 – 4ac is equal to zero then the roots are real numbers and also equal.

If the discriminant i.e b2 – 4ac is greater than zero, then the roots are real numbers and unequal.

And if discriminant i.e b2 – 4ac is less than zero then the roots are imaginary numbers.

Let us take some quadratic equations and see how we can find the nature of the roots by the using discriminant.

Example:

X2 + 3x + 9= 0

Here, on comparing with general quadratic equation we get a = 1, b = 3 and c = 9.

Discriminant, b2 – 4ac = 32 – 4 × 1 × 9 = 9 – 36 = -27.

Therefore, as discriminant is less than zero, we say that the roots are imaginary.

Y2 – 6y + 9 = 0.

On comparing with general quadratic equation we get a = 1, b = -6 and c = 9

Discriminant, b2 – 4ac = (-6)2 – 4 × 1 × 9 = 36 – 36 = 0

Therefore, as discriminant is equal to zero we get equal roots for the given quadratic equation.

Now, I think you have come to know what is the meaning of discriminant and its importance.