# 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 ax2 + bx + c is

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

### Solved Examples

Question 1: What is the discriminant of the equation x2 – 2x + 3?
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
Δ = -8