In algebra, discriminant is the common name given to the expression that appears under the square toot sign in a quadratic formula. The calculation of discriminant for polynomial of a function and its efficient generally given by the symbol delta.

It will give you the complete information of the nature of roots for any quadratic equation where a, b, and c are the rational numbers. The real roots for x-intercept can be quickly shown with a quadratic equation. Further, it is also used to check either roots of a quadratic equation are real or imaginary.

For example – The Discriminant Formula in the quadratic equation ax2 + bx + c is –

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

For a quadratic equation, the discriminant helps you to identify the total number of real solutions for a quadratic equation. This is easy to calculate with the right formula and technique. The discriminant is the part inside the square root, so it would take only a second to find what is hidden inside the square root.

Before you calculate the discriminant value for a quadratic equation you should convert it to the standard form first where one side will contain the variable or constants and other side is marked as zero.

Once it has converted to the standard form then just plug the values into formula and find the discriminant for quadratic equation. Keep in mind that it will tell you the total number of solution but it cannot explain to you what would be the solution of equation.

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

The formula for discriminant is,

Δ = b^{2} – 4ac

Δ = (-2)^{2 }– 4(1)(3)

Δ = 4 – 12

Δ = -8

The formula for discriminant is,

Δ = b

Δ = (-2)

Δ = 4 – 12

Δ = -8