₦airaland Forum

kannyluv:
......Oh my God.friends and family had made me to remain indoor and stick with my small phone..from school to house,from house to church,from house market.nothing more.......

Na so oooo!!!!

I have finally learnt that I am alone in this world.

Every body ,both family and friends ,have showed me that I am alone.

My aim is to try to stay alive,and healthy,and as well, make it( by the grace of God) ,so that family and friends would recognize me again

LordIsaac:
I just love to hear Nigerian Maths gurus talk...they are specialist in doing what has already been done!

How is it ? Have u seen this b4?

BigotMan:
Op, by comparing your deductions with the original quadratic formula, I think the original is still minimalistic and simple to use.

Finding the zeros of a 2nd-degree polynomial is very much trivial in the mathematical world. There is a proof that goes all the way to Niels Henrik Abel, who found the impossibility of solving a quintic polynomial (polynomials higher than 5th degree).

You should do more work on Abel's proof, maybe to the possibility of solving n-dimensional polynomials.


CHEERS

Thanks

moblix:
Ur first equation is wrong,Y = F(X) = X^2 - (7/12) - (10/12).
Were u put x,DAT shows DAT UR solution is wrong.
Dis is d correction
Y=F(X)=X^2-(7/12)X-(10/12)

Na typo error. U should know that

Makasis Tutorials

Today,we shall deal with the quadratic formula popularly known as almighty formula.

This formula is used to factorize and solve for the solutions ( real roots ) of any quadratic equation whose discriminant is not negative.

For countless years now, almighty formula always appears in this form
-b + √[b^2 - 4ac] / 2a
or
-b - √[b^2 - 4ac] / 2a.

This is nothing, but the fact that we normally express a general quadratic equation in the form given below
aX^2 + bX + c = 0, so that the principal of completing the square would apply for the derivation of the formula.

Suppose a general quadratic equation is expressed as a function F(X) = 0 ,where F is the quadratic Polynomial in X variable ,then how can we derive the quadratic formula without changing its original form?

This poses serious challenges to the methods used in the derivation of almighty formula,since no method could find its way.

However, I ( Mr Makasi Chinedu ) have developed a way we could follow so as to be able to derive a quadratic formula when represented as a function.

Derivation Of Almighty Formula When A Quadratic Equation Is Expressed As F(X) = 0

As we have expressed the general quadratic equation in the form F(X) = 0 ,then it is possible that a formula

F'(X) = +or--√[F(X)^2 - 4F(X)]

which represents the quadratic formula could be derived.

Proof:

Let F(X) =0 be a monic quadratic equation.

In this way, it is evident that we have already made the coefficient of the first term of F ( the quadratic polynomial) unity. That is ,

F( X ) = 0.............…...1

Now ,we let Y represents the LHS of equation 1 ,I.e,

Y = F ( X ) ...................2

Take the first order ordinary derivative of Y . That is ,

dY / dX = F'( X )...............3

Multiply the result of this differentiation by 1/2 ,I.e,

( dY / dX ) / 2 = F'( X ) / 2

( dY / 2dX ) = F'( X )............4

Raise both sides of equation four to 2 to have

(dY / 2dX )^2 = ( F'(X) / 2 )^2

(dY / 2dX )^2 = F'( X )^2 / 4.....................5

Now add both equation one and five. That is ,

F( X ) + ( dY / 2dX )^2 = F'( X )^2 / 4

Now take F(X) to the RHS to have

(dY / 2dX )^2 = F'( X )^2 / 4 - F( X )

Find the common denominator from the RHS. That is

( dY / 2dX )^2 = [ F'( X )^2 - 4F( X ) ] / 4

Take the square root and of both sides ,I.e,

√( dY / 2dX )^2 = +/- √[ F'( X )^2 - 4F( X ) ] / √4

(dY / 2dX) = +/- √[ F'( X )^2 -4F( X ) ] / 2

Now ,we clear out the fraction by multiplying both sides by 2 . That is

2( dY / 2dX ) = +/- 2√[ F'( X )^2 - 4F( X ) ] / 2

Which reduces to

dY / dX = +/- √[ F'( X )^2 - 4F( X )

Recall that

dY / dX = F ' ( X )

So in place of dY / dX from the LHS, we replace it with F ' ( X ) to have

F ' ( X ) = +/- √[ F ' ( X )^2 - 4F( X ) ]

This then becomes our Formula ( a.k.a almighty formula ) .

Lol!!!! Are you perplexed ? Don't be for i am to show you the veracity of this magic by given the few examples below.

Example 1

12X^2 - 7X - 10 = 0

Solution

First, make the question given to you a monic quadratic by dividing by 12 ,I.e,

X^2 - (7/12)X - (10/12) = 0

Here , the monic quadratic represents F(X) .

So, let

Y = F(X) = X^2 - (7/12)X - (10/12)

We work with the right hand side .

F( X ) = X^2 - (7/12)X - (10/12)

Differentiate F( X ) to have

F ' ( X ) = 2X - (7/12)

Now put 2X - (7/12) into F'(X)
In the formula ,I.e,

2X-(7/12) =+/- √[ (2X-7/12)^2 - 4F( X ) ]also recall that

F( X ) = X^2 - (7/12)X - (10/12 )

So in place of F(X) in the formula,we put the monic quadratic expression,i. E,

2X-(7/12) = +/-√[(2X - 7/12)^2 -4(X^2 -7/12X - 10/12)]

Let us evaluate the expressions inside for clarity.

(2X - 7/12)^2 - 4( X^2 - 7/12X - 10/12 )

Now expansion d to have

4X^2 - 7/3X + 49/144 - 4X^2+7/3X + 40/12

Taking like terms reduces the expression to

49/144 - 40/12

By LCM we have

529/144

So,we put our result in place of the expression inside the square root ,I.e,

2X - 7/12 = +/- √[ 529 / 144 ]
2X - 7/12 = - √[529] / √[144 ]
2X - 7/12 = [+/- 23] / 12

Divide by 2 to have

X = (7÷24) + or - (23÷24)
X = ( 7 + or - 23 ) ÷ 24

So X = 5 ÷ 4 or -2 ÷ 3

Visit my math blog to learn more @ makasistutors..com

Makasis Tutorials

Read more in my math blog @
Makasistutors..com

I believe that interested students of mathematics have painstakingly studied my former write-ups on factoring a difference of squares and sum or difference of cubes. If so,then we go to the other type of algebraic factorization .

Factoring A quadratic Trinomial

When an algebraic expression involves three terms,with the index of the first team 2 ; the index of the middle terms 1,then such an expression is called quadratic expression . See the true form of a quadratic trinomial in the expression below,

aX^2 + bX + C...............1

Is it not so clear that the first(quadratic)term has 2 as its exponent?
Is it not also clear that the second(linear)term has 1 as its power( or index )?

It is on this note that this expression is called a quadratic expression.

Note that the number of terms involved in this expression is three hence, the expression is also called a quadratic trinomial or simply ,a quadratic polynomial.

But this quadratic expression holds only if 'a' among the other coefficients ''b' and 'c' is not zero,otherwise it is a linear expression.

Factoring a quadratic expression s of two types viz:

* Factoring a non perfect square trinomial

*Factoring a perfect square trinomial

Each of these are to be treated one after the other.

Factoring a non perfect square trinomial.

Example 1

12X^2 - 7X - 10

Solution

This expression is not a perfect square quadratic trinomial owing that the first and last term have no square roots .

We will factorise this expression with the use of two distinct methods viz:

* AC method
*Matrix arrangements

By AC Method

Multiply A and C term of the quadratic trinomial to have AC ,I.e,

A×C = AC.......1
But from the expression, A = 12, while C = -10. So we substitute into equation 1 to have

12 × -10 = -120

Look for two factors of -120 whose sum is the same as the middle term -7 ,I.e,

AC = a × c .............2

a + c = b.................3

where 'a' and 'c' are two different numbers whose product is the same as AC ,while b is the middle term.

Now we find the pairs of factors of AC = -120 ,.I.e,

-120 = -120 × 1...............4
-120 = -60 × 2 ........……....5
-120 = -40 × 3..................6
-120 = -30 × 4...................7
-120 = -24 × 5...................8
-120 = -20 × 6..…....…........9
-120 = -15 × 8..…..............10

The equations 4,5,6,7,8,9,and 10 show the each pair of factors of AC = -120

Now check the pair of factor that would yield the middle term b if summed together.

Form the list of the factors, it os obvious that equation 10 is the equation that will satisfy our interest.

Now we let :

a = -15
c = 8

So we substitute these figures into equation 3 to have

-15 + 8 = b

But

b = -7

So,

-15 + 8 = -7

Which is the same as the middle term,i.e,

-15X + 8X = -7X

Now plug into -7X in the original expression to have

12X^2 -15X + 8X - 10

Note : this substitution changes nothing since the originality
Of the given expression is maintained .

Now group the expression into two binomials,i.e,

( 12X^2 -15X ) + ( 8X - 10 )

Look for a common factor in each of the binomial,i.e,

3X( 4X - 5 ) + 2(4X - 5 )

Here ,the binomial expression inside these brackets must be the same. Now pick out one of the binomials in the bracket ,I.e, ( 4X - 5 )

Also pick out the terms outside the brackets to have
( 3X + 2 ).

Set these two factors into a product form and stop!

( 4X - 5 )( 3X + 2 )...…...........11

This expression 11 shows the binomial factors of the original expression.

Because the original expression is not a perfect square trinomial,its binomial factors must differ.

To be continued

Vanquay:
Laura is useless no difference between her and the Kardashians

Soo much despise her personality, probably has a smelling stank Pvssy like her sister


Even the acidic waves from the Pussy_ is making the poor Nigga bald

some people are just immature by the way tbey talk. how can a responsible person use abusive words against somebody for nothing. . what has this lady done to you? why insulting her for no reason?

tufiakwa!!! nwa... Ibu alu.

may people insult your sister ( in your presence) just the way you have insulted this lady.

while u are busy using insulting, I am also busy praising them especially, the great lady here. I guess u know her.

rubbish!!!!!

Vanquay:
Laura is useless no difference between her and the Kardashians

Soo much despise her personality, probably has a smelling stank Pvssy like her sister


Even the acidic waves from the Pussy_ is making the poor Nigga bald

some people are just immature by the way tbey talk. how can a responsible person use abusive words against somebody for nothing. . what has this lady done to you? why insulting her for no reason?

tufiakwa!!! nwa... Ibu alu.

may people insult your sister ( in your presence) just the way you have insulted this lady.

I don't think that she will scare through with her dogged decision of not breaking her virginity unless she gets married.
Now a days, most men who are already made give some conditions before granting a job to some one.

Now, imagine this fine young lady, and her nice shape, with fresh skin. I don't blame any made person that is bent on having s...x with her b4 granting her a job.

But this is not fair at all. Why all that even.
is it because, things are not done well again in 9ja.

well, my lady,more power to your elbow. just pray that God's grace falls upon you.

good luck

mathematicalmakasi@gmail.com

ammyluv2002:
Well, you have every reason to be mad but remember, God gave you this success. He gave you dis ability cause He knows you can survive without your dad.

Just give him all the respect due to him and acknowledge him as your dad for your own good....holding such a serious beef will hinder your prayers & success to an extent. Don't let him hold you in captivity, he's not worth it so please let it go.

well written. I love that. but could u believe that this man in question, sometimes when we both quarrel, would go to his shrine and say some negative things against me so that his so-called god (aro bi nagu) would attack my future.

But I believe in the main God and for this reason,he is harmless.

SUPOL:
Get d work ist.



N y did u mention ur real name here?

well, it's not me sha. but the corper who puts on both NYSC crested vest and the jacket is my friend who encountered such from his father.

he is presently searching for job

I am Chukwuma Edozie,from Ogbunike, In Oyi Local government Area,Anambra State.
since I was born, I have never experienced any positive behavior from my father.
He has proved to be a difficult person.
in fact! to the best of my knowledge, he is a very cuny,greedy,and selfish human being.

He would make money but would rather invest it on harlots instead of we the children who are interested in education. In fact, one of his stupid friend had advised him one certain time to not waste his money in the name of training us in the university. " secondary school level is enough for us ", the man said. I don't know if that was what contributed in making my father to neglect me when I was in the university reading mathematics.
Even,amid my days in the versity, I used to take some bags of rice and tin of life vegetable oil to our house without receiving any ' thanks ' from any body though, my mum would sometimes appreciate. I did all those because of the money I generated in my class as a course rep.

Now I have graduated and gone for service in peace after training my self in the university.

With these experiences, I want to know if somebody would blame me if I fail to appreciate him as my father in case I get a work in the future.
Now he tries to come close to me because, he believes that I have conquered

After abandoning me in the campus to die, he still wants to reap the benefits of what he never merited.

well, I think I know what is is my mind.

when children talk u will know. wizy Na smalliii.
if Davido don joined then, him too Na pickin.

Linda all the way

[quote author=sunky2sweet post=44376833]Is wiskid another person she got a beef

yes they have problems now. serious one that even made Wizkid to say that her pussy stinks.
does that mean that Wizkid has seen her pussy to say so? that's the problem.

http://familyesperience..com/2016/04/you-still-hoesaid-wiskid-at-25-but.html

Linda versus Wiskid

no hard feelings, but I must confess that this is not necessary. people are suffering from many things like : hunger,diseases,sicknesses,etc. assist people financially and don't make people to cry for your conspicuous spending

I love the story of this lady . when I heard her story, I was impressed by that. I even learnt that she is the most happy married lady among her friends.

thank God for her
may God also grant me my heart desires,amen.

don't feel jealous _feel happy so that yours could come true

My name is Bukky Isiuzo. I am from Igbariam, In Anambra East LGA,Anambra State, but married to a lover In Ogbunike, In Oyi LGA,Anambra State.

Amid my university days, I had four female folks with me inclusive. we always walk together since we are in the same department. we are all good Catholics and believed to get married to catholic husbands. Unfortunately, one of our own got married to a rich pagan remaining three. In our year three time, another of our own got married to a rich igbo Muslim, and we became two remaining to get married. So as we were already in our final year,the pressure was much on us to get our own husbands. well, I embarked on prayers saying that my own husband would come one day. Despite the fact that I was the last to get married among my friends in that the third girl later married but, at least, God granted me all my wishes. I Prayed to :

** To get married to an Igbo person ;

** An Igbo person who hails from Anambra;

** An Anambrarian who is a good Catholic .

Thankfully, all these wishes came to pass. I got married to my lovely Chekwube who formally pretended to be an average person but, later showed up his riches after I had married him.

May the good God grant you all your heart desires, amen.
Thank God for me ooo ooooo!!!!

El-rufai has some sense in what he had said.
Your prayers or practice of religion should not be at the detriment of others

lol

Wike! Wike! Wike! ,ewoooo!

no be new thing for rivers

the wages of sin is death.

Rivers should learn from Anambrarians.
Anambra politics is more matured relative to Rivers

ApcSucks:
even your penis is not too much to lose mehn Love is overated

yes! u should have been the one. instead of u to decry wrong thing, u are there talking rubbish

Caliph69:
Congrats to them. Cultism really pays.

yes! it really pays. we need more. This time let it be their joy sticks