# Discriminant Formula

The discriminant formula is used to find the number of solutions that a quadratic equation has. In algebra, the discriminant is the name given to the expression that appears under the square root (radical) sign in the quadratic formula.

## Formula for Discriminant

The discriminant of a polynomial is a function of its coefficients and represented by capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equation where a, b, and c are rational numbers. The real roots or the number of x-intercepts is easily shown with a quadratic equation. This formula is used to find out whether the roots of the quadratic equation are real or imaginary.

The Discriminant Formula in the quadratic equation ax2 + bx + c is

 △ = b2 − 4ac

### Why is Discriminant Formula Important?

Using the discriminant, the number of roots of a quadratic equation can be determined. A discriminant can be either positive, negative or zero. By knowing the value of a determinant, the number of roots can be determined as follows:

• If the discriminant value is positive, the quadratic equation has two solutions.
• If the discriminant value is zero, the quadratic equation has only one solution.
• If the discriminant value is negative, the quadratic equation has no real solutions.

### Example Question Using Discriminant Formula

Question 1: What is the discriminant of the equation x2 – 2x + 3? Also, determine the number of solutions this equation has.

Solution:

In the equation,

a = 1 ; b = -2 ; c = 3

The formula for discriminant is,

Δ = b2 – 4ac

=> Δ = (-2)2 – 4(1)(3)

=>Δ = 4 – 12

Or, Δ = -8

Now, since the value of the determinant is negative, the equation will have no real solutions.

#### Practise This Question

Some of the nitrogen travels as inorganic ions, but the bulk of it is carried in the organic form as amino acids and related compounds.