Question

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

Answer 1

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

Answer 2

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

Answer 3

or just factor?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

how so?

Answer 8

yeah, how so?

Answer 9

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

Answer 10

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.

Answer 11

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.

Answer 12

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

Answer 13

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 :)

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

I think he fainted ._.

Answer 18

lol you ok bmf?

Answer 19

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

Answer 20

more like in 5 steps? please?

Answer 21

ok, just recovered

Answer 22

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

Answer 23

i am starting to understand the idea

Answer 24

great

Answer 25

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.

Answer 26

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

Answer 27

yes

Answer 28

okay, problema solved ^_^

Answer 29

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

Answer 30

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

Answer 31

but that's easily handled - factor it out.

Answer 32

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

Answer 33

*but not nut

Answer 34

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.

Answer 35

lol, thank you loki ^_^

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

with any luck...

Answer 40

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

Answer 41

i trust loki

Answer 42

lol

Answer 43

just your brain cells ._. LOL

Answer 44

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

Answer 45

aw...

Answer 46

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

Answer 47

well women too, but not as much though

Answer 48

depends on the girl actually ^^"

Answer 49

still though.

Answer 50

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?

Answer 51

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

Answer 52

cool

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

why ask such a question anyway?

Answer 57

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

Answer 58

exactly lol

Answer 59

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

Answer 60

lol...sad

Answer 61

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

Answer 62

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

Answer 63

ok, well, to be truthful...

Answer 64

I never drink

Answer 65

ever

Answer 66

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?

Answer 67

lol, good boy

Answer 68

does it look fresh? does it smell funny?

Answer 69

you are a good girl too

Answer 70

oh you're all good

Answer 71

^_^

Answer 72

lol, so are you

Answer 73

i think i'll cook it then go to bed

Answer 74

you can cook?

Answer 75

sorry to hijack the thread bmf

Answer 76

not really. i push buttons on the microwave

Answer 77

lol

Answer 78

:)

Answer 79

atleast that makes us all equal?

Answer 80

and I ask my neighbour to cook food for me

Answer 81

atleast I can cook an egg

Answer 82

better than nothing lol ^_^

Answer 83

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

Answer 84

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

Answer 85

oh lucky you, I just burn everything lol

Answer 86

still learning :)

Answer 87

:)

Answer 88

anyways, basket time, talk later

Answer 89

ok

Answer 90

bye

Answer 91

i;m out...bye

Answer 92

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