# Discriminant Formula

In algebra, the discriminant is the name given to the expression that appears under the square root (radical) sign in the quadratic formula. 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. For example – The Discriminant Formula in the quadratic equation ax^{2} + bx + c is

\[\LARGE \bigtriangleup =b^{2}-4ac\]

### Solved Examples

**Question 1:**What is the discriminant of the equation x

^{2}– 2x + 3?

**Solution:**

In the equation, a = 1 ; b = -2 ; c = 3

The formula for discriminant is,

Δ = b

Δ = (-2)

Δ = 4 – 12

Δ = -8

The formula for discriminant is,

Δ = b

^{2}– 4acΔ = (-2)

^{2 }– 4(1)(3)Δ = 4 – 12

Δ = -8