anonymous
  • anonymous
Calculate the sum and the product of the equation roots. Give the answer in fractions (ex: x = 3 ¾).
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[-3x ^{2}+2x+4=0\]
anonymous
  • anonymous
do you want to find the answer when you plug x in the equation?
anonymous
  • anonymous
or just factor?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • 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
  • anonymous
It wants you to understand the relationship between the roots and coefficients in a quadratic.
anonymous
  • anonymous
If you do, you can read off from that equation what you need to know without any working (well, much working).
anonymous
  • anonymous
how so?
anonymous
  • anonymous
yeah, how so?
anonymous
  • 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
  • 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
  • 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
  • anonymous
ok.... *eyes wide open, helpless face*
anonymous
  • 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
  • anonymous
\[-3x^2+2x+4=0 \iff x^2-\frac{2}{3}x-\frac{4}{3}=0\]
anonymous
  • anonymous
Then you can read off the sum and product of roots.
anonymous
  • anonymous
\[\alpha + \beta = \frac{2}{3}\]\[{\alpha}{\beta}=-\frac{4}{3}\]
anonymous
  • anonymous
I think he fainted ._.
anonymous
  • anonymous
lol you ok bmf?
anonymous
  • anonymous
loki what were you trying to say, can you summarize it please? :)
anonymous
  • anonymous
more like in 5 steps? please?
anonymous
  • anonymous
ok, just recovered
anonymous
  • anonymous
lol, he'll summarize it don't worry ^_^
anonymous
  • anonymous
i am starting to understand the idea
anonymous
  • anonymous
great
anonymous
  • 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
  • anonymous
so now he can put them equal to each other and continue.
anonymous
  • anonymous
yes
anonymous
  • anonymous
okay, problema solved ^_^
anonymous
  • anonymous
the only catch is that you have to ensure the coefficient of x^2 is 1.
anonymous
  • anonymous
he'll divide by -3 like you've said , got that andy?
anonymous
  • anonymous
but that's easily handled - factor it out.
anonymous
  • anonymous
ok, got it, nut I think I have to get drunk like loki so next time I can figure stuff faster
anonymous
  • anonymous
*but not nut
anonymous
  • 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
  • anonymous
lol, thank you loki ^_^
anonymous
  • anonymous
yeah, have a beer and mathematics will be more fun ;)
anonymous
  • anonymous
you don't need to get drunk to answer a question andrius
anonymous
  • anonymous
lol so he'll get 4 when you ask him 1+1 ._.
anonymous
  • anonymous
with any luck...
anonymous
  • 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
  • anonymous
i trust loki
anonymous
  • anonymous
lol
anonymous
  • anonymous
just your brain cells ._. LOL
anonymous
  • anonymous
drinking is bad bad bad, but you boys are just so stubborn to accept that.
anonymous
  • anonymous
aw...
anonymous
  • anonymous
I'm serious, men always do the opposite lol, wanting to try everything
anonymous
  • anonymous
well women too, but not as much though
anonymous
  • anonymous
depends on the girl actually ^^"
anonymous
  • anonymous
still though.
anonymous
  • 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
  • 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
  • anonymous
cool
anonymous
  • anonymous
wait, if the weather's cold, then I guess it's safe
anonymous
  • anonymous
it'll keep the chicken cooled just like leaving it in a fridge.
anonymous
  • anonymous
there's no difference, the only small difference is temperature and where you place it.
anonymous
  • anonymous
why ask such a question anyway?
anonymous
  • anonymous
I am kind of lost on how beer, chikens and men wanting to do the opposite relate to each other
anonymous
  • anonymous
exactly lol
anonymous
  • anonymous
see what happens when you drink? you lose the relation between subjects and things.
anonymous
  • anonymous
lol...sad
anonymous
  • anonymous
evidence = loki's question , no more drinking for you
anonymous
  • anonymous
but he has a point, what does that question got to do with drinking?
anonymous
  • anonymous
ok, well, to be truthful...
anonymous
  • anonymous
I never drink
anonymous
  • anonymous
ever
anonymous
  • 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
  • anonymous
lol, good boy
anonymous
  • anonymous
does it look fresh? does it smell funny?
anonymous
  • anonymous
you are a good girl too
anonymous
  • anonymous
oh you're all good
anonymous
  • anonymous
^_^
anonymous
  • anonymous
lol, so are you
anonymous
  • anonymous
i think i'll cook it then go to bed
anonymous
  • anonymous
you can cook?
anonymous
  • anonymous
sorry to hijack the thread bmf
anonymous
  • anonymous
not really. i push buttons on the microwave
anonymous
  • anonymous
lol
anonymous
  • anonymous
:)
anonymous
  • anonymous
atleast that makes us all equal?
anonymous
  • anonymous
and I ask my neighbour to cook food for me
anonymous
  • anonymous
atleast I can cook an egg
anonymous
  • anonymous
better than nothing lol ^_^
anonymous
  • anonymous
though I'm still learning, I want to >_<
anonymous
  • 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
  • anonymous
oh lucky you, I just burn everything lol
anonymous
  • anonymous
still learning :)
anonymous
  • anonymous
:)
anonymous
  • anonymous
anyways, basket time, talk later
anonymous
  • anonymous
ok
anonymous
  • anonymous
bye
anonymous
  • anonymous
i;m out...bye
anonymous
  • anonymous
Try www.aceyourcollegeclasses.com

Looking for something else?

Not the answer you are looking for? Search for more explanations.