## Introduction to Discriminant Calculator

Discriminant calculator is an online digital tool that is used for finding the discriminant of roots of quadratic equations using its coefficient values. Our tool **computes the quadratic equation formula** to find whether the nature of the root is real or imaginary in less than a minute.

## What is Discriminant?

Discriminat is the component in the quadratic equation that **find discriminant of the nature of roots** in quadratic equation.

Resultantly, it gives real roots or imaginary or maybe it gives them both real or imaginary roots. For Discriminant D or Δ symbol is used in the quadratic equation formula for finding roots.

## Rules Followed by Nature of Roots Calculator:

The discriminant calculator uses the following **discriminant rule of the quadratic equation** to find the root value.

$$ ax^2 + bx + c \;=\; 0 \; \; , b^2 − 4ac $$

Here,

a,b,c are the coefficients of the quadratic equation

## Stepwise Evaluation Process of Discriminant Finder

Nature of roots calculator uses a quadratic equation formula to find out the polynomial roots of the given equation quickly and easily. You can get the solution of various types of polynomial coefficients discriminant roots in a couple of seconds.

When you **enter the polynomial coefficients** in the discriminate calculator, it starts to identify the given data.

After identification, the discriminant calculator finds the quadratic equation and then compares the given equation with its standard form of quadratic equation to determine the coefficients first.

After that, it **substitutes the coefficients** in the discriminant formula as b^{2}-4ac to find the discriminant roots. There are three cases through which it tells whether a given equation gives real or imaginary root values.

### Case 1: When b^{2} - 4ac >0

When you add the coefficient in the discriminant math calculator, if its result is a positive number then the quadratic equation gives real or positive but unequal roots.

### Case 2: When b^{2} -4ac <0

When you **add the coefficient** in the nature of roots calculator, if its solution gives a negative number then the quadratic equation gives imaginary or negative roots.

### Case3 : When b^{2} - 4ac =0

When you add the coefficient in the discriminant calculator, if its result is equal to zero then the quadratic equation gives real and equal positive roots.

## Find the Discriminant - An Example

To get more clarity about this concept let's observe an **example of a quadratic equation** along with its solution in detail. Now you would know how to calculate discriminant and understand the results of the discriminant finder.

### Example 1:

Determine the discriminant of the following equation using the formula b^{2}-4ac.

$$ x^2 + 5x + 4 \;=\; 0 $$

**Solution:**

From the above equation,

$$ a \;=\; 0, b \;=\; 5 \;and\; c \;=\; 4 $$

Therefore,

$$ b^2 - 4ac \;=\; (5)^2 - 4(1)(4) \;=\; 25 - 16 \;=\; 9 $$

When the discriminant is than 0 then there are two different real roots.

### Example 2:

Determine the discriminant of the following equation using the formula b^{2}-4ac

$$ -3x^2 + 6x - 3 \;=\; 0 $$

**Solution:**

From the above equation,

$$ a \;=\; -3, \; b \;=\; 6 \;and\; c \;=\; -3 $$

$$ b^2 - 4ac \;=\; (6)^2 - 4(3)(-3) $$

$$ \;=\; 36 -36 \;=\; 0 $$

### Example 3:

Determine the discriminant of the following equation using the formula b^{2}-4ac.

$$ -x^2 + 3x - 3 \;=\; 0 $$

**Solution:**

From the above equation

$$ a \;=\; -1, \; b \;=\; 3 \;and \; c \;=\; -3 $$

Therefore,

$$ b^2 - 4ac \;=\; (3)^2 - 4(-1)(-3) $$

$$ \;=\; 9 - 12 \;=\; -3 $$

So, there are no real roots and the discriminant is less than zero. There are exactly two distinct imaginary roots.

## How to Use the Discriminant Calculator

The discriminate calculator has a user-friendly interface so that you can easily **use it to evaluate** quadratic equation questions in calculus in a few seconds.

Before adding the input value to this discriminant math calculator, you must follow some simple steps to get an amazing experience during the calculation process. These steps are:

- Enter the coefficient of a value in the input box of the discriminant finder.
- Enter the coefficient of the b value in the input box
- Enter the coefficient of the c value in the input box
- Click on the “Calculate” button to get the desired result of your given Discriminant quadratic problem
- If you want to try out our nature of roots calculator for practice, then you can use the load example for better understanding
- Click on the “Recalculate” button to get a new page for solving more Discriminant root problems

## Final Result of Discriminate Calculator

Discriminant calculator gives you the **solution to quadratic equation root** problems whenever you add the input in it. With that, It provides you with solutions to the Discriminant values in complete detail in no time. It may contain as

- Result option gives you a solution for the Discriminant problem
- Possible step option provides all the steps that are used in the evaluation process for the quadratic equation method problem with the explanation.

## Benefits of Using the Discriminant Math Calculator

You need to do the manual calculation to find the discriminant to the given quadratic questions due to its complex calculation process.

The nature of roots calculator gives you multiple **benefits** whenever you use it for the evaluation of real or imaginary roots from quadratic equation problems in no time. These benefits are

**Trustworthy tool**

Discriminant finder is a reliable tool as It always gives you accurate results every time with no mistakes in the evaluation of quadratic equation problems

**Speedy calculator**

It saves your time and effort from **doing lengthy computations** by the hand of quadratic roots equation

**Simple interface**

Discriminate calculator is a simple design tool that helps you to get the solution to real or imaginary roots easily

**Free calculator**

It is a free tool so you do not need to pay the charge before using it to calculate the discriminant method

**Education tool**

You should use our Discriminant calculator for finding the discriminant of various types of quadratic equation root examples to get a strong grip on this concept.