## Solving Quadratic Equations Calculator

**Introduction:**

An equation of the type

**ax2 + bx + c**, where

**a**,

**b**,

**c**are variables with

**a**not equal to zero is called as quadratic equations. In a quadratic equation calculator, once the quadratic equation is given as the input in the calculator, the result will be manipulated by the calculator in the form of graph. Let us learn about solving quadratic equation calculator with a solved examples.

Types of quadratic equation:

**1. Pure quadratic equation :**

The numerical coefficient cannot be zero. If b=0 then the quadratic equation is called as a ‘pure’ quadratic equation

**2. Complete quadratic equation:**

If the equation having x and x2 terms such an equation is called a ‘complete’ quadratic equation. The constant numerical term ‘c’ may or may not be zero in a complete quadratic equation.

**Example,**x2 + 5x + 6 = 0 and 2x2 - 5x = 0 are complete quadratic equations.

**Properties of roots of solving a Quadratic Equation:**

- The sum of roots of a quadratic equation is,

- The multiples of the roots of a quadratic equation is, (x1)(x2) = c/a

In the quadratic equation formula,

**b2-4ac is discriminant,**

There are three things may occur according to the

**discriminant**.

**b2- 4ac > 0,**the equation having two different real roots.

**b2- 4ac = 0,**the quadratic equation having two equal roots.

**b2- 4ac < 0,**the equation does not have real roots. The roots are imaginary.

Sample Problem for Solving Quadratic Equation Calculator:

Solve the quadratic equation by factoring method and find roots?

3x2-4x-4=0

**Solution:**

**Step 1:**Multiply the coefficient of x2 and the constant term,

3 * -4 = -12 (product term)

**Step 2:**Find the factors for the product term

-12 → -6 * 2 = -12 (factors -6 and 2)

-12 → -6 + 2 = -4 (-4 is equal to the coefficient of x)

**Step 3:**Split the coefficient of x as -4

3x2 - 4x - 4 = 0

3x2 - 6x + 2x - 4 = 0

**Step 4:**Taking the common term 3x for the first two term and 2 for the next two terms

3x(x - 2) + 2(x - 2) = 0

(3x + 2) (x - 2) = 0.

Now set (3x + 2) = 0; 3x = -2; x = -2/3

(x - 2) = 0; x = 2.

The roots are

**x = -2/3 and 2.**