In mathematics, a discriminant is a value that can be used to determine the nature of the roots of a polynomial equation. Specifically, it is the determinant of the matrix of coefficients of the equation.

For example, the discriminant of x^{2}+px+q=0 is p^{2}-4q. If the discriminant is positive, the equation has two real roots.

If negative, it has no real roots; and if zero, it has a repeated root. In the case of a cubic equation, such as x^{3}+px^{2}+qx+r=0, the discriminant is p^2q^2-4q^3-4pr^2+18pqr-27r^2.

## Cubic equation

A cubic equation with a discriminant of zero has a repeated root; one with a positive discriminant has three distinct real roots; and one with a negative discriminant has one real root and two complex conjugate roots.

The discriminant can also be used to determine the stability of a critical point of a function. If the discriminant of the Hessian matrix at that point is positive, the critical point is a local minimum.

If negative, it is a local maximum; and if zero, it is either a saddle point or an inflexion point. There are also discriminant test for other equations,

Variables: p, q, r

## What makes a math equation discriminant?

The answer lies in its ability to help us identify the roots of a polynomial equation. This value is determined by the determinant of the matrix that houses the coefficients of the equation in question.

In other words, the discriminant tells us how many and what type of roots an equation has. Let’s take a look at how this works with a couple of examples.

### Example 1: Determining the Number of Real Roots

Let’s start with a simple quadratic equation:

y = x^{2} + 5x + 6

We can use what we know about the discriminant to determine how many roots this equation has and what type they are.

## Advancement of the Calculator

**Discriminant Calculator **is an online tool that helps you to find the discriminant of a quadratic equation. It is a simple and easy-to-use calculator that can be used by anyone.

The discriminant of a quadratic equation is a very important concept in mathematics. It is used to determine the nature of the roots of the equation.

## Basic Formula for a Discriminant Calculator

The discriminant of a quadratic equation is the numerical value that results from subtracting the square of the term containing the unknown x from the product of the coefficients of the two terms that contain x. This value provides information about the number and type of roots that the equation has.

It is usually denoted by the symbol “D” and is given by the following formula:

D = b^{2} – 4ac

Where “b” is the coefficient of the linear term, “a” is the coefficient of the quadratic term, and “c” is the constant term.

## How would you solve a quadratic equation that has no C?

There are a few ways to solve a quadratic equation that has no C. One way is to use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

Another way is to factor the equation, which can be done by factoring out the greatest common factor, or by using the quadratic formula. Finally, you can graph the equation to find the x-intercepts, which will give you the solution to the equation.

## Distinct

If the discriminant is positive, then the roots are real and distinct. If the discriminant is zero, then the roots are real and equal.

## Imaginary

If the discriminant is negative, then the roots are imaginary.

## Discriminant Calculator for quadratic equations & polynomials

**Discriminant calculator** is a free online tool that displays the discriminant value for the given quadratic equation.

This discriminant solver tool calculates the roots of the quadratic equation from the given coefficients (a, b, and c). It also provides a detailed step-by-step solution for the quadratic equation by using the quadratic formula.

Input: a = 5, b = 2, c = 3

Output: The discriminant is -23 and the roots are -1+2i and -1-2i.

## The Discriminant of a Quadratic Equation

In algebra, the discriminant of a quadratic equation is a number that is associated with the coefficients of the equation. It helps to determine the nature of the roots of the equation. The discriminant is usually denoted by Δ (delta).

## How to find the roots of a quadratic equation on a calculator?

First, make sure your calculator is in “Quadratic” mode. To do this, press the “Mode” button and scroll until you see “Quad.”

Next, enter the coefficients of your quadratic equation into the calculator. For example, if your equation is x^2 + 4x + 3 = 0, you would enter “1, 4, 3.”

Once you have entered the coefficients, press the “Calculate” button. Your calculator will then display the roots of your equation. In the example above, the roots would be -1 and -3.