# Quadratic Equation Calculator

Quadratic Equation Calculator is used to determine the roots of a given quadratic equation. A quadratic equation is an algebraic equation in one variable and the degree of the equation is 2.

## What is a Quadratic Equation Calculator?

Quadratic Equation Calculator is an online tool that helps to solve the given quadratic equation and find its roots. The standard form of a quadratic equation is given by ax^{2} + bx + c = 0. Here, x is the variable, a and b are coefficients and c is the constant. To use the * quadratic equation calculator*, enter the values in the input boxes.

### Quadratic Equation Calculator

NOTE: The coefficient of x^{2} should not be zero.

## How to Use Quadratic Equation Calculator?

Please follow the steps below to solve the quadratic equation using the quadratic equation calculator.

**Step 1:**Use Cuemath's online quadratic equation calculator.**Step 2:**Enter the values in the given input boxes of the quadratic equation calculator.**Step 3:**Click on the**"Calculate"**button to solve the given quadratic equation.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does the Quadratic Equation Calculator Work?

When we solve a quadratic equation we get two values of x. These values are known as roots. There are 4 methods to find the roots of a quadratic equation. These are completing the square method, factorizing the quadratic equation, using the quadratic formula, and the graphing technique. Out of these, the quickest method to find the roots of the given quadratic equation is by using the quadratic formula. Further, various important inferences can also be drawn, regarding the nature of the roots by applying this formula. If the quadratic equation is given as ax^{2} + bx + c = 0, then the quadratic formula is given by:

x = (-b ± √(b^{2} - 4ac))/2a.

We can find the nature of the roots by analyzing the discriminant (D). This is part of the quadratic formula and is given as follows:

D = b^{2} - 4ac.

- D > 0, the roots of the quadratic equation are real and distinct.
- D = 0, the roots are real and equal.
- D < 0, the roots do not exist, that is, the roots are imaginary.

## Solved Examples on Quadratic Equations

**Example 1:** Solve the quadratic equation x^{2} + 5x + 6 = 0 and verify it using the quadratic equation calculator.

**Solution:**

Given: a = 1, b = 5, c = 6

x = (-b ± √(b^{2} - 4ac))/2a.

x = (-5 ± √(5^{2} - 4 × 1 × 6))/2 × 1.

x = -2, -3

Therefore, the roots of the given quadratic equation are -2, -3. Further, as D > 0 the roots are real and distinct.

**Example 2:** Solve the quadratic equation 2x^{2} - 4x + 2 = 0 verify it using the quadratic equation calculator.

**Solution:**

Given: a = 2, b = -4, c = 2

x = (-b ± √(b^{2} - 4ac))/2a.

x = (-(-4) ± √((-4)^{2} - 4 × 2 × 2))/2 × 2.

x = 1, 1

Therefore, x = 1 Further, as D = 0, the roots are real and equal.

Similarly, you can try the quadratic equation calculator to solve the following quadratic equations:

- 2x
^{2}+ x − 3 = 0 - x
^{2}+ 10x − 11 = 0

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