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# Quadratic Formula Calculator

Enter the coefficients of * x* in the quadratic formula and equation calculator to find its roots.

Table of Contents:

This advanced quadratic equation and formula solver computes the roots of a quadratic equation. It also gives the detail of the whole process along with a plotted graph.

## What is a Quadratic equation?

Quadratic means involving the power of two. A quadratic equation is:

*“ A polynomial expression which has the maximum degree of variable as 2.”*

A quadratic equation is of the form ax^{2 }+ bx + c = 0. Where a, b, and c are the coefficients and are known. While variables like “x” are unknown.

## Quadratic equation formula

To find the values of X, roots, we use a formula known as the quadratic formula:

Where **√**(b^{2} - 4ac) is known as a discriminant.

## Nature of the roots

The value of the discriminant determines the nature of the roots whether they are real or imaginary (complex) roots. Here is a guide to learn it beforehand:

- If discriminant > 0 , roots are real
- If discriminant = 0, one real root
- If discriminant < 0, imaginary roots

## How to solve Quadratic equations?

**Example:**

Solve 6x^{2} + 4x + 2 = 0.

**Solution:**

**Step 1:** Identify the Coefficients.

a = 6, b = 4 and c = 2

**Step 2:** Use the quadratic formula.

So, the roots are complex. These radicals can be further solved as