Need help with Alpha and Beta (1 Viewer)

[boongsta]

Hey guys first post I really need help with understanding the roots of equations ... and can someone possibly explain what the Alpha and Beta formula's mean

like seriously how could alpha+beta = -b/a ??? I got preliminary finals coming up next week and this I cannot seem 2 understand ... i can just remember it but i'd really appreciate it if someone could please explain the reasoning behind it thanks

 

[Pace_T]

ive never asked myself this but ill try to asnwer it logically

quadratic eqn = ax^2 - x(sum of roots) + product of roots
= ax^2 - bx + c

roots = -b/a = sum of roots
c/a = product of roots

or some shit like that i dunno lol

 

[Sparcod]

Hey guys first post I really need help with understanding the roots of equations ... and can someone possibly explain what the Alpha and Beta formula's mean

like seriously how could alpha+beta = -b/a ??? I got preliminary finals coming up next week and this I cannot seem 2 understand ... i can just remember it but i'd really appreciate it if someone could please explain the reasoning behind it thanks

alpha and beta are the roots. there is reasoning to it but it's not important to know.

Also, the product of roots =c/a

Good luck with your finals.

 

[Dreamerish*~]

Just remember the formulae:

α + β = -b/a
αβ = c/a

Are you doing the polynomials chapter? Because if you are, there are much much harder questions involving not only α and β.

 

[tryx]

If you have a quadratic, let its 2 roots be <b>p</b> and <b>q</b>.
That means that in factored form, the quadratic is (x - p)(x - q).
(x-p)(x-q) = x^2 -x(q + p) + pq

We don't know what this quadratic's coefficiants are, so let them be a, b, c
Thus getting the quadratic ax^2 + bx + c. This quadratic is the same as the one we had to begin with, so we can equate them.

ax^2 + bx + c = x^2 -x(q + p) + pq

To make things fair, we divide the LHS by a to make both sides monic.

x^2 + (b/a)x + (c/a) = x^2 -x(q + p) + pq

Then by equating coeffs. we get our familiar results.
Sum or roots (p +q ) = -b/a
and so forth.

PS: I can't type alpha and beta, and a and b would clash with other places, so p is alpha and q is beta.

 

[boongsta]

thanks a lot guys

i reckon this stuff u guys typed out would really help ... although it looks a little weird on the comp ill scribble it out later to understand it and hopefully ill master this stuff for the test ... thanks a lot guys cant believe how quick the responses are and the quality of responses

have u guys got any good sites for math to help study? as im getitng sick of reading from books

thanks again

BTW im not doing the poly chapter atm im just revising over old papers and looking at individual formula's ... do u know if these root things get harder throughout the 2 unit course in year 12? tomorrow is my last day for year 11 classes but no more maths class so hmmm

 

[Dreamerish*~]

i reckon this stuff u guys typed out would really help ... although it looks a little weird on the comp ill scribble it out later to understand it and hopefully ill master this stuff for the test ... thanks a lot guys cant believe how quick the responses are and the quality of responses

have u guys got any good sites for math to help study? as im getitng sick of reading from books

thanks again

BTW im not doing the poly chapter atm im just revising over old papers and looking at individual formula's ... do u know if these root things get harder throughout the 2 unit course in year 12? tomorrow is my last day for year 11 classes but no more maths class so hmmm

Oh, 2-unit, sorry. Yeah it doesn't get too hard then.

I was thinking 3U polynomials, which kind of kill you.

 

[insert-username]

Off the top of my head, in 2U you just cover quadratic roots, so basically just that. In 3U, you expand right out to cubics and quartics as well. Blargh.


I_F

 

[boongsta]

ouch sounds like a brainkiller ... my mate that sometimes helps me does all this crazy crap in 3 unit cant believe how hard it is plus all the other subjects we gotta keep on top of ... software design and development is kinda similar to maths except its really basic and just another way of doing it ... and a little more on the artistic mind than pure maths ... just thoughts lol