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
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