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

- anonymous

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

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- anonymous

\[-3x ^{2}+2x+4=0\]

- anonymous

do you want to find the answer when you plug x in the equation?

- anonymous

or just factor?

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## More answers

- anonymous

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

- anonymous

It wants you to understand the relationship between the roots and coefficients in a quadratic.

- anonymous

If you do, you can read off from that equation what you need to know without any working (well, much working).

- anonymous

how so?

- anonymous

yeah, how so?

- anonymous

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\[c={\alpha}{\beta}\]

- anonymous

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.

- anonymous

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.

- anonymous

ok.... *eyes wide open, helpless face*

- anonymous

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 :)

- anonymous

\[-3x^2+2x+4=0 \iff x^2-\frac{2}{3}x-\frac{4}{3}=0\]

- anonymous

Then you can read off the sum and product of roots.

- anonymous

\[\alpha + \beta = \frac{2}{3}\]\[{\alpha}{\beta}=-\frac{4}{3}\]

- anonymous

I think he fainted ._.

- anonymous

lol you ok bmf?

- anonymous

loki what were you trying to say, can you summarize it please? :)

- anonymous

more like in 5 steps? please?

- anonymous

ok, just recovered

- anonymous

lol, he'll summarize it don't worry ^_^

- anonymous

i am starting to understand the idea

- anonymous

great

- anonymous

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.

- anonymous

so now he can put them equal to each other and continue.

- anonymous

yes

- anonymous

okay, problema solved ^_^

- anonymous

the only catch is that you have to ensure the coefficient of x^2 is 1.

- anonymous

he'll divide by -3 like you've said , got that andy?

- anonymous

but that's easily handled - factor it out.

- anonymous

ok, got it, nut I think I have to get drunk like loki so next time I can figure stuff faster

- anonymous

*but not nut

- anonymous

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.

- anonymous

lol, thank you loki ^_^

- anonymous

yeah, have a beer and mathematics will be more fun ;)

- anonymous

you don't need to get drunk to answer a question andrius

- anonymous

lol so he'll get 4 when you ask him 1+1 ._.

- anonymous

with any luck...

- anonymous

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

- anonymous

i trust loki

- anonymous

lol

- anonymous

just your brain cells ._. LOL

- anonymous

drinking is bad bad bad, but you boys are just so stubborn to accept that.

- anonymous

aw...

- anonymous

I'm serious, men always do the opposite lol, wanting to try everything

- anonymous

well women too, but not as much though

- anonymous

depends on the girl actually ^^"

- anonymous

still though.

- anonymous

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?

- anonymous

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

- anonymous

cool

- anonymous

wait, if the weather's cold, then I guess it's safe

- anonymous

it'll keep the chicken cooled just like leaving it in a fridge.

- anonymous

there's no difference, the only small difference is temperature and where you place it.

- anonymous

why ask such a question anyway?

- anonymous

I am kind of lost on how beer, chikens and men wanting to do the opposite relate to each other

- anonymous

exactly lol

- anonymous

see what happens when you drink? you lose the relation between subjects and things.

- anonymous

lol...sad

- anonymous

evidence = loki's question , no more drinking for you

- anonymous

but he has a point, what does that question got to do with drinking?

- anonymous

ok, well, to be truthful...

- anonymous

I never drink

- anonymous

ever

- anonymous

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?

- anonymous

lol, good boy

- anonymous

does it look fresh? does it smell funny?

- anonymous

you are a good girl too

- anonymous

oh you're all good

- anonymous

^_^

- anonymous

lol, so are you

- anonymous

i think i'll cook it then go to bed

- anonymous

you can cook?

- anonymous

sorry to hijack the thread bmf

- anonymous

not really. i push buttons on the microwave

- anonymous

lol

- anonymous

:)

- anonymous

atleast that makes us all equal?

- anonymous

and I ask my neighbour to cook food for me

- anonymous

atleast I can cook an egg

- anonymous

better than nothing lol ^_^

- anonymous

though I'm still learning, I want to >_<

- anonymous

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

- anonymous

oh lucky you, I just burn everything lol

- anonymous

still learning :)

- anonymous

:)

- anonymous

anyways, basket time, talk later

- anonymous

ok

- anonymous

bye

- anonymous

i;m out...bye

- anonymous

Try www.aceyourcollegeclasses.com

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