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. 

                                                                                                                                  

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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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 

Multipication on finger tips trick

Every time we see the sign of multiplication we start using the method we were taught in school.
It is time consuming but saves our brain fuel.
But if we use our brain then we can save time

What is Multiplication
Multiplication is addition.
Yes it is.

Consider this example
Multiply 2 by 3
2* 3 .

It means that add 2 three times or add 3 two times
2+2+2 = 6
   or
 3 + 3 = 6

So if we want to multiply 27 by 39 then it means addition of 27 to  39 time or addition of 39 to 27 term

there are diffrent ways of multiplication we can use depending upon our way of understanding

for e.g.

                           2  8
                         ×3  5 
                            140
                            84×
                            980
    
use this technique

28  is 20 +  8
35  is  30 + 5 

Now first multiply the exterior terms mean that 30 × 20 = 600
then multiply cross term                                     20 ×5 = 100
                                                                        30×8  =  240
in last                                                                8  ×5 =    40
 final result is addition                                      28×35=    980

Square of number starting with 5?

 In our daily life we use number 5 many times.In this method you will going to learn how to get square of number starting with 5 like 51, 52 53 etc and so on.

51*51=2601

RHS =  Square of number at ones place here it is  1*1=1 =>01

LHS =  25 + the number at ones place here its 1 =>(25 + 1)=26

answer is LHS/RHS = 26/01 =>2601

Now

52 * 52 = 2704

RHS =2 * 2 =04

LHS = 25 + 2=27

Answer is 27/04 = 2704

Now

54 * 54 = 2916

RHS = 4 * 4 = 16

LHS =25 + 4 = 29

Answer is 2916

Try to find square of 53 , 55, 56 ,57 etc

Square of number ending with 5?

The most easiest way to get square of number ending with 5.

It is based on Vedic maths.

By using this trick you can get square of any number ending with five within fraction of second

Consider a number

15*15 = . 225

Wondering how its works?

 Right hand side  it is always 25

LHS  = (number) * (number +1)

 here it is 1 * (1+1)= 2

so the answer is  2/25 (backslash is for indication only) so we get 225

next  number is 25

RHS =25

LHS= 2*(2+1)=>2*3=6

Answer is 625

Similarly

square of 35

3*(3+1)/25

1225

try the square of these number and share the result in Comments

45,55,65,75,85,95

Prime number Check Trick

 

Prime number check.

Prime numbers are those numbers which are only divisible by one and itself.

1,35,7,11,13,17 and so on……..

For small numbers it is easy to say whether number is Prime number or not.

But for large number like 1189 it is quite difficult to check its prime number test

But here is the trick that can check Prime number test within fraction of seconds.

If the number contains 2 or multiple of 2 at ones place it is not a prime number.

Like 2782, 1322, 1238, 9876 etc.

Whatever is the number use this trick.

Let the number be 89

Divide this number by 8 and then 9, 8+9=17 and 7+1=8

First step      = 89/8 not divisible

Second step = 89/9 not divisible

3^rd step          = 89/17 not divisible

Final step     =89/8 not divisible

So the number is Prime number.

Now check number 139

 Important Note   If number contains one at any position doesn’t check the number for one.

First step         =139/3 not divisible

Second Step   = 139/9 not divisible

Third step       = 139/13 not divisible

Final step        = 139/4 not divisible.

So the number is Prime number.

Now check the number 453

First step       = 453/4 not divisible

Second Step = 453/5 not divisible

Third step     = 453/3 = 151.

Since it is divisible so the number is not a Prime number.

This tricks works for a large number also. It will not take your much time to practice this trick.

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Trick to get square of two digit number?

How to square the double digit number

This trick use simple multiplication and addition to get square of two digit number with in fraction of second. You can use this method to double any number from 11 to 99.Here we go

Let us start with number 14

Square of 14= 14 ×14

  14

×14

 196

Right Hand side digit  =        4 * 4 = 16 ,So the first digit is 6 and one carry

Second digit  =   2(1×4) + 1 = 9

Third digit  =  1 ×1 = 1

So the answer is 196

General rule for multiplication

                               

                                               2^nd digit 2(1*4) + 1 carry from first digit

                                                            1        4             4 * 4 = 16

3rd digit  (1*1 + carry2^nd digit)             1         4     

                                                          1   9     6

now 23* 23

first digit 3*3 = 9
2nd digit = 2(2*3) + carry from first here it is 0 so  2nd digit = 12
3rd digit  = 2 * 2 + carry from second digit here it is 1 = 5
answer is                 529

Try  23 27 87  99 34 and share the result with others in comment

Trick to remember the table of 19.

 Trick to remember the table of 19.

Since it is easy to remember the table of 20. So you can obtain the table of 19 from table of 20.

To get table of 19 just minus the number from 20’s table for e.g. if you want to get value of 19 × 5 just minus the 5 from 20 × 5

19×5 = (20 × 5) -5 = 95.

 20 × 1 =  20                                  19 ×1 =  (20-1)    =      19

 20 × 2 =  40                                  19 × 2 = (40-2)    =      38

 20 × 3  = 60                                  19 × 3 = (60-3)    =      57

20 × 4  =  80                                  19 × 4 = (80-4)   =      76

20 × 5  =  100                                19 × 5 = (100-5) =      95

20 × 6  =  120                                19 ×6 = (120-6)  =     114

20 × 7  =  140                                19 ×7 = (140-7)  =     133

20 × 8  =  120                                19 ×8 =(160-8)   =     152

20 × 9  =  180                                19 ×9 = (180-9)  =     171

20 × 10 = 200                               19 ×10 = (200-10) =     200

This trick can be further extended to 199,299,399 …… 1999.

Try it and share with others.