QES Abbreviation

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Popular abbreviations of QES:

Searching for QES abbreviation / QES full form leads to different results in different categories. The below table illustrates the popular acronyms among them.

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What does QES mean?

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.