How to Solve Quadratic Equation

  How to Solve Quadratic Equation

What is the meaning of solving Quadratic Equation?

Answer is quite simple "In sample  manner finding the roots of equation"

Now what are  roots of quadratic Equations.

Roots are those values of "x" at which the equation is satisfied for e.g.

                     2x² -8x + 5 = 0   

roots of this equations means those values of x at which this equation is satisfied 

let x1 and x2 be those values of x 

then when we put these values in equation it must satisfy it 

                                     L.H.S=R.H.S 

 

                                   Solving Equation

First we have to find the nature of roots.For this we have to find discriminant

Roots can be real,equal and complex

Following Equation is the genric quadratic equation

                             ax²+bx + c = 0   

                             Discriminant or D is given by

                                D =   b²- 4ac

                If

                             D > 0 two  roots are real

                             D = 0  roots are equal

                             D < 0 two roots are complex 

For e.g.

Case 1:

                                      for the equation

                                        2x² -8x + 5 = 0  

                          Compare it with generic quadratic equation   ax²+bx + c = 0  

                                 a= 2 ,b= -8,c= 5 

                              so D =  (-8)² -4*2*5

                                       = 64 -40

                                       =24

                                      24 >0

                    s        o it has two real roots 

Case 2:

                           Now consider this equation

                               x² -2x + 5 = 0  

                                so a= 1,b= -2,c = 5

                               D=   (-2)² -4*1*5

                                   = 4 -20

                                   = -16

                                 Since -16 <0 font="" nbsp="">

                             so D is negative it has two complex roots 

 

Case 3 :

        

                               x² -2x + 1 = 0  

                              a=1,b=-2,c=1

                            D   =   (-2)² -4*1*1

                                 =  4-4

                                   =0

                           Since D=0 so it has two equal roots

 

                  

         

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