Math Is Fun Forum

soha

Real Member

Registered: 2006-07-07

Posts: 2,530

root prove

If one root of the equation

is 3 times the other then prove that

Last edited by soha (2010-04-01 03:09:42)

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"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"
- David O. McKay

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: root prove

Hmmm...

Remember:Whenever any Relation between Roots is given, its always Best to Start with Sum and Products of the Roots...
This will help u solve Most of the Problems in the Examination!

Let one root be K.
Hence, other root will be 3K.

Sum of Roots: K+3K=-p  (-b/a)
===>  4K=-p
===>  16K^2=p^2 (square both sides)
===>  48K^2=3p^2 (multiply both sides by 3) .......(1)

Product of Roots:K.3K=q  (c/a)
===>  3K^2=q
===>  48K^2=16q .......(2)

Result from (1) & (2)!

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If two or more thoughts intersect, there has to be a point!

soha

Real Member

Registered: 2006-07-07

Posts: 2,530

Re: root prove

Sum of the roots is p ???? Why -p??

where is 3 p^2?

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"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"
- David O. McKay

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: root prove

If equation is

then,

where is 3 p^2

===>  48K^2=3p^2 (multiply both sides by 3) .......(1)

Last edited by ZHero (2010-04-03 18:56:14)

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If two or more thoughts intersect, there has to be a point!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: root prove

Hi soha;

Here is another idea, if one root is 3 times the other then it has factor of:

expand that

Now you have the equations:

substituting:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

soha

Real Member

Registered: 2006-07-07

Posts: 2,530

Re: root prove

after that , how did you get 48....??

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"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"
- David O. McKay

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: root prove

...............
Product of Roots:K.3K=q  (c/a)
===>  3K^2=q
===>  48K^2=16q .......(2)

Result...........

after that , how did you get 48....??

Silly Girl!!!!

Multiply both sides of 3K^2=q by 16 and u'll get eq.........(2) above

now, as....
48K^2=3p^2..........(1)
48K^2=16q............(2)

hence....
3p^2=16q

Last edited by ZHero (2010-04-02 18:58:13)

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If two or more thoughts intersect, there has to be a point!

soha

Real Member

Registered: 2006-07-07

Posts: 2,530

Re: root prove

ufff!!!!!!!!!!!!

It was so easy!!!!!!!!!!!

goT it now!!

Thanks!!

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"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"
- David O. McKay