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 = 0 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 nature of roots can be determined as follows:

  • If the discriminant value is positive, the quadratic equation has two real and distinct solutions.
  • If the discriminant value is zero, the quadratic equation has only one solution or two real and equal solutions.
  • 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 = 0? Also, determine the number of solutions this equation has.


Given, x2 – 2x + 3 = 0

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 < 0

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


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