## Sunday, August 25, 2013

## 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.

###
* 2x*^{2} -8x + 5 = 0

*2x*^{2}-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

####
* ax*^{2}+bx + c = 0

*ax*^{2}+bx + c = 0####
* *Discriminant or D is given by

####
D **= *** b*^{2}- 4ac

**=**

*b*^{2}- 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

###
* 2x*^{2} -8x + 5 = 0

*2x*^{2}-8x + 5 = 0###
Compare it with generic quadratic equation *ax*^{2}+bx + c = 0

*ax*^{2}+bx + c = 0###
*a= 2 ,b= -8,c= 5 *

*a= 2 ,b= -8,c= 5*###
*so D = (-8)*^{2} -4*2*5

*so D = (-8)*^{2}-4*2*5###
* = 64 -40*

*= 64 -40*###
* =24*

*=24*###
* 24 >0*

*24 >0*### s o it has two real roots

###
*Case 2:*

*Case 2:*

#### Now consider this equation

###
* x*^{2} -2x + 5 = 0

*x*^{2}-2x + 5 = 0###
* so a= 1,b= -2,c = 5*

*so a= 1,b= -2,c = 5*###
* D= **(-2)*^{2} -4*1*5

*D=*

*(-2)*^{2}-4*1*5###
* = 4 -20*

*= 4 -20*###
* = -16*

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

###
** ** so D is negative it has two complex roots

###
*Case 3 :*

*Case 3 :*

###
* ** x*^{2} -2x + 1 = 0

*x*^{2}-2x + 1 = 0###
* * a=1,b=-2,c=1

###
* **D = **(-2)*^{2} -4*1*1

*D =*

*(-2)*^{2}-4*1*1###
* = 4-4*

*= 4-4*###
* =0*

*=0*###
* ** *** Since D=0 so it has two equal roots**

####
*<
*

*<*

## Tuesday, July 30, 2013

### 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**

*ax*where^{2}+ bx + c = 0,*a, b,*and*c*are constants."**Quad stand for 2 any equation which have highest power of 2 is quadratic equation**

For e.g.

*5x*^{2}+ 6x + 8= 0

*2x*^{2}-8x + 5 = 0Now consider this example

*5x*^{2}+ 5x +15Is 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.

*5x*^{2}+ 5x =8Is 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 = x*^{2}+ 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 = x

^{2}+ 5x + 6=0

=>x

^{2}+ 5x + 6=0

=>x

^{2}+ 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

## Sunday, June 30, 2013

### 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__

## Friday, March 8, 2013

### 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

## Monday, March 4, 2013

### 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.

## Sunday, March 3, 2013

### 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 = 1

__6__,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 = 1

**6**
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

## Saturday, March 2, 2013

### 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.

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