Understanding Quadratic Equations

  Iam explaining  quadratic equation in most simple way

"Quadratic Equation" consist of two terms Quadratic and Equation
Dictionary meaning of Quadratic means "Of, relating to, or containing quantities of the second degree."

So Quadratic means term containing power of two

Equations means  " The act or process of equating or of being equated"

Quadratic Equations means "An equation in which one or more of the terms is squared but raised to no higher power, having the general form ax² + bx + c = 0, where a, b, and c are constants."

Quad stand for 2 any equation which have highest power of 2 is quadratic equation
For e.g.

                            5x² + 6x + 8= 0

                           2x² -8x + 5 = 0   

Now consider this example

5x² + 5x +15

Is it a quadratic equation
Not its not a quadratic equation because it is not equating to any thing.

For a quadratic equation it must be eual to something

for e.g.

5x² + 5x =8

 Is it a quadratic equation
Yes it is a quadratic equation

 How to solve Quadratic Equation

Before this we should know why we solve and what will we get after solving this equation
Solving a Quadratic equation means getting the values which will satisfy this equation
and those values which satisfy the equations are  known as roots.

For a Quadratic equation there can be only two roots possible for a single quadratic equation
 Since quad means two so only two roots are possible for a quadratic equation.

Consider this example 


  
                              let  y = x² + 5x + 6 = 0 

 we need to solve it or we have to find the roots of this equation.

roots are those values of x at which y = 0

                                                       
                                                        y =  x² + 5x + 6=0
                                      =>x² + 5x + 6=0
                                      =>x² + 3x+2x + 6=0
                                    => x(x+3) +2(x+3)  =0
                                  => (x+3)(x+2)=0
so roots are x= -3 and -2

if we place these roots in equation in place of x we ger

         first take x = -3  
       then              LHS          (-3) ² + 5(-3) + 6
                                             9     -15    +6
                                             -6+6        
                                            = 0
LHS = RHS