Sunday, August 25, 2013

Roman Number System and conversion of European into Roman System

Number system is the mathematical way of representing the things, items by symbols.
For e.g.  In European Number system we represent the numbers of apple in following way

Roman numeral is the earliest number system that is still in use. 


Sunday, August 11, 2013

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 



                                   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


                             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 >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  


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

                                 =  4-4


                           Since D=0 so it has two equal roots












Related Posts Plugin for WordPress, Blogger...