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

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

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

BecomeMyFan=D
 3 years ago
Best ResponseYou've already chosen the best response.0that 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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0If 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\[c={\alpha}{\beta}\]

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0The 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.

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0Your 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.

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

sstarica
 3 years ago
Best ResponseYou've already chosen the best response.0LOL, 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 :)

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

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

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

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

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0Imagine 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.

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

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0When 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.

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

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

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

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

BecomeMyFan=D
 3 years ago
Best ResponseYou've already chosen the best response.0well, 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

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0what 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?

sstarica
 3 years ago
Best ResponseYou've already chosen the best response.0it 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

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

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

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

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

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

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

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

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

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

lokisan
 3 years ago
Best ResponseYou've already chosen the best response.0it 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?

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

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

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

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

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

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

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

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

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

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

BecomeMyFan=D
 3 years ago
Best ResponseYou've already chosen the best response.0no, 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

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

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

sammi789
 3 years ago
Best ResponseYou've already chosen the best response.0Try www.aceyourcollegeclasses.com
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