naturalwaves:


A newly discovered method last month.
You just pick the coefficient of x, span it in the middle and equate to the C term.
E. G
If you are to solve
X²-16x+48=0
16 is the coefficient of x.
Half of 16 is 8.

We just split this 8 into two parts and write
(8+u)(8-u)=48

U²=16
U= +/- 4

Just subatitute +/-4 into (8+u) and (8-u)
You will get 12 and 4 everytime.

Therefore,
X=4 or x =12 is the solution of the parent quadratic equation
This method was discovered worldwide few weeks ago.

What's the name of this method pls?

Jodha:


What's the name of this method pls?

It has not be named yet. However, it is a derivative of some old Babylonia method, Viata's formulas, Greek and French approaches and so on but I like to call it Loh's method or Loh's alternative quadratic method as it was discussed by Professor Po-Shen Loh. He was the coach of the USA team that won International Mathematics Olympiad back to back. He is a professor of mathematics at Carnegie Mellon University.

naturalwaves:


A newly discovered method last month.
You just pick the coefficient of x, span it in the middle and equate to the C term.
E. G
If you are to solve
X²-16x+48=0
16 is the coefficient of x.
Half of 16 is 8.

We just split this 8 into two parts and write
(8+u)(8-u)=48

U²=16
U= +/- 4

Just subatitute +/-4 into (8+u) and (8-u)
You will get 12 and 4 everytime.

Therefore,
X=4 or x =12 is the solution of the parent quadratic equation
This method was discovered worldwide few weeks ago.

Uncle sobo
You simply modified completing the square
You never jam correct quadratic equations that gives complex number

You really tried with the explanation so I doff my hat

enawt:

Uncle sobo
You simply modified completing the square
You never jam correct quadratic equations that gives complex number

You really tried with the explanation so I doff my hat

Sobo ke? Lmao
The entire methods for solving quadratic are all related.
It is a faster approach for teaching students particularly if the coefficient of X is an even number, it can be solved in less than 30 seconds.

You also need to make sure that the coefficient of X² is 1 before you start @Jodha

naturalwaves:

Sobo ke? Lmao
The entire methods for solving quadratic are all related.

Agreed @ Bolded

It is a faster approach for teaching students particularly if the coefficient of X is an even number, it can be solved in less than 30 seconds.

Not advisable though, you only teach students with high intellect and numerical prowess fast mathematical methods.

enawt:
Agreed @ Bolded

Not advisable though, you only teach students with high intellect and numerical prowess fast mathematical methods.

It isn't complex.

The idea behind this method was to stop that process of guessing for factors and doing trial and error in the case of factorisation method.


https://www.youtube.com/watch?v=ZBalWWHYFQc&t=4s

naturalwaves:


It isn't complex.

The idea behind this method was to stop that process of guessing for factors and doing trial and error in the case of factorisation method.


https://www.youtube.com/watch?v=ZBalWWHYFQc&t=4s

I totally get you mahn. I just know it becomes complex when you tackling harder quadratic equations. There are many equations you can't solve using factorization method

enawt:

I totally get you mahn. I just know it becomes complex when you tackling harder quadratic equations. There are many equations you can't solve using factorization method

Yeah sure but this method works well for a wide range because of that middle interval method. The method is basically for secondary school students but still works fine for even decimal answers that an ordinary factorisation method would not solve.

elegantslayer:
pls help me solve this....3/2m^2-m-4=0....pls mathematicians should help,I need to he'll my cousin with d answer cos have tried..

3M² -2M -8 =0

3M² - 6M + 4M - 8 = 0

(M-2)(3M+4) = 0

M = 2 or -4/3

naturalwaves:

It has not be named yet. However, it is a derivative of some old Babylonia method, Viata's formulas, Greek and French approaches and so on but I like to call it Loh's method or Loh's alternative quadratic method as it was discussed by Professor Po-Shen Loh. He was the coach of the USA team that won International Mathematics Olympiad back to back. He is a professor of mathematics at Carnegie Mellon University.

Oh i see... thanks a lot ...

For once I've learnt something new here ..

naturalwaves:

Sobo ke? Lmao
The entire methods for solving quadratic are all related.
It is a faster approach for teaching students particularly if the coefficient of X is an even number, it can be solved in less than 30 seconds.

You also need to make sure that the coefficient of X² is 1 before you start @Jod.ha

If it isn't like the question...the op asked...what do we do?

Jodha:


If it isn't like the question...the op asked...what do we do?

Give any example of a quadratic equation that is not in that form. Let me solve it using that method. Preferably, give one whose coefficient of X² is not 1.

Jodha:

Oh i see... thanks a lot ...

For once I've learnt something new here ..

elegantslayer ,i asked the lady earlier if it was;

3/(2m²- m - 4


of (3/2)m² - m - 4...... correct

Had it been you told me it was the latter, it's very easy.

Multiply all through by 2

2 x (3/2)m² - 2 x m - 2 x 4

3m² - 2m - 8

That's a quadratic equation

It can be solved using Factorization, Completing the square or Almighty formula method.

So let us use the almighty formula because it gives the best result and the most trusted; even in real and complex answer.

-b ± √(b² - 4ac) / 2a

a= 3, b = -2, c= -8

-(-2) ± √((-2)² - (-1)(4x3x8))/ 2x3

2± √(4 + 96) / 6

2±√100 / 6

2±10 / 6

2+10 / 6 or 2-10 /6

12/6 or -8/6

m = 2 or -4/3

naturalwaves:

Give any example of a quadratic equation that is not in that form. Let me solve it using that method. Preferably, give one whose coefficient of X² is not 1.

-5/2X²+2X-3=7

Can yhu pls throw more light on the "De Moivre's" theorem?

Kylekent59:
I asked the lady earlier if it was;

3/(2m²- m - 4


of (3/2)m² - m - 4

Had it been she told me it was the latter, it's very easy.

Multiply all through by 2

2 x (3/2)m² - 2 x m - 2 x 4

3m² - 2m - 8

That's a quadratic equation

It can be solved using Factorization, Completing the square or Almighty formula method.

So let us use the almighty formula because it gives the best result and the most trusted; even in real and complex answer.

-b ± √(b² - 4ac) / 2a

a= 3, b = -2, c= -8

-(-2) ± √((-2)² - (4x3x(-)) / 2x3

2± √(4 + 96) / 6

2±√100 / 6

2±10 / 6

2+10 / 6 or 2-10 /6

12/6 or -8/6

m = 2 or -4/3

Yhure right....I also feel using almighty formula is the best...

Jodha:


-5/2X²+2X-3=7

Can yhu pls throw more light on the "De Moivre's" theorem?

You can get the PDF on Google and download the file.

Almighty formular is the best. When you go deeper in maths, like university, your 200 - 500 level, you would do real analysis and your results would be in complex form like ( 2±3i)...

Even ODE; topics like second order differential equation

Jodha:


-5/2X²+2X-3=7

Can yhu pls throw more light on the "De Moivre's" theorem?

Okay, Let me try this,
Multiply through by 2 and modify equation to obtain,
5x² -4x +20=0
Observe that the coefficient of x² is not 1
So,
divide through by 5 to get,
X²- (4/5)X + 4= 0
Using Loh's theorem,
Half way through 4/5 is 0.4
Hence,
( 0.4+u)(0.4-u)=4
0.16- u²=4
u²= -3.84
u= square root of (-3.84)
u= square root of [(3.84)(-1)]
u= 1.96i (Note: In complex number, square root of -1= i)
Our answers are (0.4+1.96i) and (0.4-1.96i)
As for De Moivre's theorem, let me give you one of the videos from Eddie Woo. He takes his time to explain concepts.
Check through some of his other videos. He is a good teacher.

https://www.youtube.com/watch?v=Qha-Lsdj5xo

naturalwaves:

Okay, Let me try this,
Multiply through by 2 and modify equation to obtain,
5x² -4x +20=0
Observe that the coefficient of x² is not 1
So,
divide through by 5 to get,
X²- (4/5)X + 4= 0
Using Loh's theorem,
Half way through 4/5 is 0.4
Hence,
( 0.4+u)(0.4-u)=4
0.16- u²=4
u²= -3.84
u= square root of (-3.84)
u= square root of [(3.84)(-1)]
u= 1.96i (Note: In complex number, square root of -1= i)
Our answers are (0.4+1.96i) and (0.4-1.96i)
As for De Moivre's theorem, let me give you one of the videos from Eddie Woo. He takes his time to explain concepts.
Check through some of his other videos. He is a good teacher.

https://www.youtube.com/watch?v=Qha-Lsdj5xo

Using almighty formula i got X as 1.56 or -2.36

naturalwaves:

Okay, Let me try this,
Multiply through by 2 and modify equation to obtain,
5x² -4x +20=0
Observe that the coefficient of x² is not 1
So,
divide through by 5 to get,
X²- (4/5)X + 4= 0
Using Loh's theorem,
Half way through 4/5 is 0.4
Hence,
( 0.4+u)(0.4-u)=4
0.16- u²=4
u²= -3.84
u= square root of (-3.84)
u= square root of [(3.84)(-1)]
u= 1.96i (Note: In complex number, square root of -1= i)
Our answers are (0.4+1.96i) and (0.4-1.96i)
As for De Moivre's theorem, let me give you one of the videos from Eddie Woo. He takes his time to explain concepts.
Check through some of his other videos. He is a good teacher.

https://www.youtube.com/watch?v=Qha-Lsdj5xo

I watched the video...thanks alot...

So i solved it again...look...

Jodha:


I watched the video...thanks alot...

So i solved it again...look...

The solution is not correct dear.
How do you find the square root of a negative number?
There must be a complex number in your solution but there is none. You should get the exact thing I have below when you use quadratic formula.
Note that the answer given here is same as what I got when I used Loh's methods.

naturalwaves:

The solution is not correct dear.
How do you find the square root of a negative number?
There must be a complex number in your solution but there is none.

It's been long i calculated...but i thought...

Oh well... that's the only issue right?

Jodha:


It's been long i calculated...but i thought...

Oh well... that's the only issue right?

I have edited my comment to come with solution. Look up, you will see it. Better still, let me repaste the quadratic solution again.

naturalwaves:

I have edited my comment to come with solution. Look up, you will see it. Better still, let me repaste the quadratic solution again.

Can yhu pls calculate it again without multiplying both sides by 2 .... It's possible to solve it with the fraction right?

Yet the answer yhu got using the almighty formula... seems quite different from the one yhu got us the new method...

I don't think the method is reliable

Jodha:


Can yhu pls calculate it again without multiplying both sides by 2 .... It's possible to solve it with the fraction right?

Yet the answer yhu got using the almighty formula... seems quite different from the one yhu got us the new method...

I don't think the method is reliable

It is not different. It is the same thing dear. Simplify the answers gotten from the quadratic. It is same as what I got.

2(1+2 root 6i)/5, or 2(1-2root6i)/5
0.4(1+2root 6i), 0.4(1-2root6i)
0.4 +1.96i or 0.4-1.96i

Did you see that it is the same thing now?

The method is very very reliable.
If you know who Po-Shen Lo is, you wouldn't even say the method isn't reliable.

naturalwaves:

It is not different. It is the same thing dear. Simplify the answers gotten from the quadratic. It is same as what I got.

2(1+2 root 6i)/5, or 2(1-2root6i)/5
0.4(1+2root 6i), 0.4(1-2root6i)
0.4 +1.96i or 0.4-1.96i

Did you see that it is the same thing now?

The method is very very reliable.
If you know who Po-Shen Lo is, you wouldn't even say the method isn't reliable.

But a quadratic equation can be solved with fraction while using the almighty formula right?

Jodha:


But a quadratic equation can be solved with fraction while using the almighty formula right?

Yes now.
Check your solution.
Your base is even wrong. Your denominator is supposed to be 2 x - 5/2 and not 2 x 10.

Kylekent59:


elegantslayer ,i asked the lady earlier if it was;

3/(2m2- m - 4


of (3/2)m2 - m - 4...... correct

Had it been you told me it was the latter, it's very easy.

Multiply all through by 2

2 x (3/2)m2 - 2 x m - 2 x 4

3m2 - 2m - 8

That's a quadratic equation

It can be solved using Factorization, Completing the square or Almighty formula method.

So let us use the almighty formula because it gives the best result and the most trusted; even in real and complex answer.

-b ± √(b2 - 4ac) / 2a

a= 3, b = -2, c= -8

-(-2) ± √((-2)2 - (-1)(4x3x8))/ 2x3

2± √(4 + 96) / 6

2±√100 / 6

2±10 / 6

2+10 / 6 or 2-10 /6

12/6 or -8/6

m = 2 or -4/3

Help solve this also, 1. 3^√x = 8x.

2. 3^x + 5^x = 17x

redpencil:
M=4 or M= √3/2


---Solutions To Questions like this can be found in WAEC/CBT app. Check my signature (Please note: it is not free.)

Help solve this two also, 1. 3^√x = 8x.

2. 3^x + 5^x = 17x

redpencil:
I'm Sorry for the previous mistake.

Please note, this exercise is a modulation of a polynomial equation.

To solve this, we need to use cubic formula.


Let's solve your equation step-by-step.

2m3+8m2−3=0
(Please study the cubic formula below and input the values).

Step 1: Use cubic formula.

m=−3.901454,−0.671286,0.57274
Answer:
m=−3.901454,−0.671286,0.57274

Help solve this two also, 1. 3^√x = 8x.

2. 3^x + 5^x = 17x

naturalwaves:

I am on the road and cannot grab a pen but let me use my phone to solve it.
The answer is m=-4/3 or m=2
Check the pictures atta he'd for a comprehensive solution.

Help solve this two also, 1. 3^√x = 8x.

2. 3^x + 5^x = 17x

naturalwaves:


A newly discovered method last month.
You just pick the coefficient of x, span it in the middle and equate to the C term.
E. G
If you are to solve
X²-16x+48=0
16 is the coefficient of x.
Half of 16 is 8.

We just split this 8 into two parts and write
(8+u)(8-u)=48

U²=16
U= +/- 4

Just subatitute +/-4 into (8+u) and (8-u)
You will get 12 and 4 everytime.

Therefore,
X=4 or x =12 is the solution of the parent quadratic equation
This method was discovered worldwide few weeks ago.

Help solve this two also, 1. 3^√x = 8x.

2. 3^x + 5^x = 17x