- Full Form:
**Quadratic Equation Solver** - Category:
**Mathematics**

**प्रश्न:(QES) का फुल फॉर्म**

The Polynomial equations with one variable whose highest degree is two are called **Quadratic Equations**. In layman’s terms, equations that can be expressed as ax^2 +bx +c =0 are called Quadratic Equations.

## Forms of quadratic equation

There are three main forms of quadratic equation viz.

- Standard Form- quadratic equation in ax^2 +bx +c =0 form is called standard form. Here a, b, and c are constants and x is the variable.
- Factored Form- y= a(x-e)(x-f); here a, e, and f are constants and x is the variable.
- Vertex Form- y= a(x-g)^2 +k; here a, g, and k are constants and x is the variable.

## Methods to Solve Quadratic Equation (QES)

Three commonly used methods can be elucidated e.g. using the quadratic formula, the factoring method, and completing the square method. All the methods are demonstrated as follows with an example-

### Factoring Method

In this method, the equation is rewritten in factored form. Let’s solve x^2 -5x +6 =0 for x.

- Firstly, rewrite the equation as x^2 -3x -2x +6 =0
- Then factor the equation as (x-3)(x-2) =0
- Therefore, the values of x will be either 3 or 2.

This method is sometimes called the ‘middle-term factor’

### Using Quadratic Formula

For the equation ax^2 +bx +c =0, the quadratic formula to determine the values of x is cited as

X = [−b ± √(b2 − 4ac)] /2a

this formula is also known as the ‘Sridharacharya Formula’

here, the term (b2 − 4ac) is called ‘discriminant’ as this determines whether the values of x will be real or complex

if the discriminant is positive then x will obtain two real values, and x will obtain a single real value if the discriminant is 0. But, the negative value of the discriminant implies that x will obtain complex values.

### Completing the Square

For example, to solve x^2 +8x +15=0 the following steps are executed

- The equation is rewritten as x^2 +2.4.x +16 -1 =0
- Therefore, it becomes (x+4)^2 =1
- Square rooting both sides, x+4 = ±1
- Therefore, the values of x will be 3,5.

## Real-life examples

The trajectory of a free-falling body, equation of circles, hyperbola, etc. will derive a quadratic equation to be solved by one of the three ways devised above.

## All Full Forms of QES:

you will see all full forms of QES in Hindi in the following table. Please note that all definitions are listed in popularity-wise.

- Quarterly Employment Survey (Business Terms)
- Quality Evaluation (Exams & Tests)
- Quasi Elastic Scattering (Chemistry)
- Questar Energy Services (Companies & Corporations)
- Quality Expert Statement (Business Terms)
- Quarterly Employment Statistics (Census & Statistics)
- Quality Evaluation System (Specifications & Standards)
- Quinn Electrical Services (Companies & Corporations)
- Quanta Energized Services (Companies & Corporations)
- Quick Erect Scaffold (Healthcare)
- Quality Execution System (Business Management)
- Quarterly Economic Survey (Business Terms)
- Quality, Environment And Safety (Terms)
- Qualcomm Enterprise Services (Companies & Corporations)
- Qatar Exoplanet Survey (Astronomy & Space Science)
- Quality, Environmental, And Social (Companies & Corporations)
- Queen Elizabeths School (Universities & Institutions)
- Qualified Electronic Signature Pack (Security)
- Quality Engineered Systems Limited (Companies & Corporations)
- Quadratic Expenditure System (Accounting)
- Quantitative Execution Strategies (Business Terms)
- Quota Exchange System (Data Storage)
- Quality Excellence System (Business Management)
- Quebec Esperanto Society (Regional Organizations)
- Quality Electrical Systems, Inc (Companies & Corporations)

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