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Calculate the sum and the product of the equation roots. Give the answer in fractions
(ex: x = 3 ¾).
 3 years ago
 3 years ago
Calculate the sum and the product of the equation roots. Give the answer in fractions (ex: x = 3 ¾).
 3 years ago
 3 years ago

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BecomeMyFan=DBest ResponseYou've already chosen the best response.0
\[3x ^{2}+2x+4=0\]
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
do you want to find the answer when you plug x in the equation?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
that is what I dont know, because this question came as it is, I know how to do quadratic equations, but I just dont understand what the question wants from me
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
It wants you to understand the relationship between the roots and coefficients in a quadratic.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
If you do, you can read off from that equation what you need to know without any working (well, much working).
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
If you have the quadratic equation,\[x^2+bx+c=0\]if\[\alpha \]and\[\beta \]are the roots, then you'd also have\[(x\alpha)(x\beta)=0\]If you expand this, you get\[x^2(\alpha + \beta)+{\alpha}{\beta}=0\]Comparing the first and second equations, you have that they will be identical equations if and only if their coefficients are identical. Then\[x^2+bx+c=x^2(\alpha + \beta) + {\alpha}{\beta}\]if and only if\[b=(\alpha + \beta)\]and\[c={\alpha}{\beta}\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
The coefficient of x is related to the sum of roots, and the coefficient of x^0 (i.e. c) is related to the product of the roots.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Your equation differs only in that it has a coefficient for x^2 (i.e.3). But guess what? You can get rid of it by dividing your equation through by 3.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
ok.... *eyes wide open, helpless face*
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
LOL, what he's trying to say is you can get the equation you have in the form of the general equation when you divide by 3 :)
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
\[3x^2+2x+4=0 \iff x^2\frac{2}{3}x\frac{4}{3}=0\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Then you can read off the sum and product of roots.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
\[\alpha + \beta = \frac{2}{3}\]\[{\alpha}{\beta}=\frac{4}{3}\]
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
I think he fainted ._.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
loki what were you trying to say, can you summarize it please? :)
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
more like in 5 steps? please?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
ok, just recovered
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
lol, he'll summarize it don't worry ^_^
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
i am starting to understand the idea
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Imagine alpha and beta are the roots of some quadratic equation. Then you can write the quadratic as a product of its factors\[(x\alpha)(x\beta)\]Expand and see that it equals\[x^2(\alpha + \beta)x + {\alpha}{\beta}\]So, you should see from the form that the coefficient of x in a quadratic is related to the SUM of the roots, while the constant is related to the PRODUCT of the roots.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
so now he can put them equal to each other and continue.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
okay, problema solved ^_^
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
the only catch is that you have to ensure the coefficient of x^2 is 1.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
he'll divide by 3 like you've said , got that andy?
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
but that's easily handled  factor it out.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
ok, got it, nut I think I have to get drunk like loki so next time I can figure stuff faster
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
When you're just given the quadratic\[ax^2+bx+c\]and it's not set equal to anything, to get at the relationship for the roots, you have to factor out, rather than divide (there's nothing on the other side of an equals sign to divide). So in this case,\[ax^2+bx+c=a[x^2+\frac{b}{a}x+\frac{c}{a}]\]and you'd relate the roots to the stuff in the brackets.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
lol, thank you loki ^_^
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
yeah, have a beer and mathematics will be more fun ;)
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
you don't need to get drunk to answer a question andrius
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
lol so he'll get 4 when you ask him 1+1 ._.
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
well, I can see loki is smart, and he just said I should have a beer and maths will be more fun, so, I guess I have nothing to lose
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
just your brain cells ._. LOL
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
drinking is bad bad bad, but you boys are just so stubborn to accept that.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
I'm serious, men always do the opposite lol, wanting to try everything
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
well women too, but not as much though
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
depends on the girl actually ^^"
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
what happens if you leave raw chicken out of the fridge for two days but the weather's cold? do you think it's safe to cook?
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
it depends, you must check if there's any fungus left on top , smell it ; if it's good then yes, if not then you must imediately throw it away
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
wait, if the weather's cold, then I guess it's safe
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
it'll keep the chicken cooled just like leaving it in a fridge.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
there's no difference, the only small difference is temperature and where you place it.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
why ask such a question anyway?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
I am kind of lost on how beer, chikens and men wanting to do the opposite relate to each other
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
see what happens when you drink? you lose the relation between subjects and things.
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
evidence = loki's question , no more drinking for you
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
but he has a point, what does that question got to do with drinking?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
ok, well, to be truthful...
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
it doesn't. it's just that i spent $6 on some chicken but then went out for dinner and i'm wondering if i should now cook it before bed or throw it out?
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
does it look fresh? does it smell funny?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
you are a good girl too
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
i think i'll cook it then go to bed
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
sorry to hijack the thread bmf
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
not really. i push buttons on the microwave
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
atleast that makes us all equal?
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
and I ask my neighbour to cook food for me
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
atleast I can cook an egg
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
better than nothing lol ^_^
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
though I'm still learning, I want to >_<
 3 years ago

BecomeMyFan=DBest ResponseYou've already chosen the best response.0
no, I am kidding, I can actually make any kind of food, at one time I even considered becoming a cook LOL. so, now I can bake cakes, complex meals and all kind of desserts
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
oh lucky you, I just burn everything lol
 3 years ago

sstaricaBest ResponseYou've already chosen the best response.0
anyways, basket time, talk later
 3 years ago

sammi789Best ResponseYou've already chosen the best response.0
Try www.aceyourcollegeclasses.com
 3 years ago
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