Hey guys! Root help! (1 Viewer)

[borkis04]

Hey guys! I need your help again sorry

I have a minor problem with the Sums and Product of Roots..

I know how to do the ά + β and άβ..but I came down the the last question in a series of questions..

I know how to:
Alpha + beta
Alpha times Beta
Alpha^2 + Beta^2
Etc etc
But I cant figure how to to
Alpha minus Beat..ie ά – β…with the equation say 3x^2 + 6x – 3 = 0…how do u find
ά – β

Thanks in advance!...again.

 

[icycloud]

Let a = alpha, b = beta

a^2 + b^2 = (a+b)^2 - 2ab

(a-b)^2 = a^2 - 2ab + b^2
= (a^2 + b^2) - 2ab
= (a+b)^2 - 2ab - 2ab
= (a+b)^2 - 4ab

Therefore, a-b = +/- Sqrt((a-b)^2)
= +/- Sqrt([a+b]^2 - 4ab)

(+ or - depending on which root you put as a and which root you put as b)

 

[borkis04]

ohh i see...again!

thansk mate..appreciate it!

 

[Srixon]

alpha + beta = -b over a

alphabeta = c over a

alpha^2 + beta ^2 =(alpha+ beta)^2 -2alphabeta


1 over alpha + 1 over beta = Beta + alpha over alpha beta

 

[r.haidar]

u no the title of this thread could be really misleading...

 

[borkis04]

u no the title of this thread could be really misleading...

haha i know aye! haha

thanks mate..(the guy above r.haidar...i understand now! cheers mate n hav a good 1

 

[chin music]

Let a = alpha, b = beta

a^2 + b^2 = (a+b)^2 - 2ab

(a-b)^2 = a^2 - 2ab + b^2
= (a^2 + b^2) - 2ab
= (a+b)^2 - 2ab - 2ab
= (a+b)^2 - 4ab

Therefore, a-b = +/- Sqrt((a-b)^2)
= +/- Sqrt([a+b]^2 - 4ab)

(+ or - depending on which root you put as a and which root you put as b)

Shouldnt the second line of working be (a-b)^2=a^2=2ab+b^2

 

[Trev]

Shouldnt the second line of working be (a-b)^2=a^2=2ab+b^2

No.
10chars

 

[chin music]

O i get it now. didnt see the (a-b)