This formula determines how many solutions a quadratic equation has. In algebra, the expression under the radical sign in the quadratic formula is called the discriminant.

Formula for Discriminant

The function of coefficients that can be written in terms of capital 'D' or Delta symbol (Δ) is known as discriminant of any polynomial. It indicates the nature of roots of any quadratic equation if a, b, and c are rational numbers. The number of real roots or x-intercepts can easily be proved with a quadratic equation. This formula is used to check whether the roots of the quadratic equation are real or imaginary.

The Discriminant Formula in the quadratic equation 

Why is Discriminant Formula Important?

With the aid of a discriminant, the number of roots of a quadratic equation can be determined. A discriminant can be either positive, negative or zero.With the knowledge of value of a determinant, the nature of the roots can be determined in the following manners:

• If the value of discriminant is positive, then it possesses two distinct and real solutions.

• If the discriminant value is zero, then that quadratic equation has one or two real equal solutions.

• If the discriminant value is negative, then this means that no real solutions exist for the given quadratic equation.

Example Question Using Discriminant Formula

Question 1: What is the discriminant of the equation x2 – 2x + 3 = 0? Also, determine the number of solutions this equation has.

Solution:

 

Given, 

In the equation,

a = 1 ; b = -2 ; c = 3

The formula for discriminant is,

=>Δ = 4 – 12   

Δ = -8 < 0

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