## anonymous 5 years ago Calculate the sum and the product of the equation roots. Give the answer in fractions (ex: x = 3 ¾).

1. anonymous

$-3x ^{2}+2x+4=0$

2. anonymous

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

3. anonymous

or just factor?

4. 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

5. anonymous

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

6. anonymous

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

7. anonymous

how so?

8. anonymous

yeah, how so?

9. 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$c={\alpha}{\beta}$

10. 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.

11. 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.

12. anonymous

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

13. 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 :)

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

I think he fainted ._.

18. anonymous

lol you ok bmf?

19. anonymous

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

20. anonymous

more like in 5 steps? please?

21. anonymous

ok, just recovered

22. anonymous

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

23. anonymous

i am starting to understand the idea

24. anonymous

great

25. 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.

26. anonymous

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

27. anonymous

yes

28. anonymous

okay, problema solved ^_^

29. anonymous

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

30. anonymous

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

31. anonymous

but that's easily handled - factor it out.

32. anonymous

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

33. anonymous

*but not nut

34. 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.

35. anonymous

lol, thank you loki ^_^

36. anonymous

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

37. anonymous

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

38. anonymous

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

39. anonymous

with any luck...

40. 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

41. anonymous

i trust loki

42. anonymous

lol

43. anonymous

just your brain cells ._. LOL

44. anonymous

45. anonymous

aw...

46. anonymous

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

47. anonymous

well women too, but not as much though

48. anonymous

depends on the girl actually ^^"

49. anonymous

still though.

50. 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?

51. 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

52. anonymous

cool

53. anonymous

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

54. anonymous

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

55. anonymous

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

56. anonymous

why ask such a question anyway?

57. anonymous

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

58. anonymous

exactly lol

59. anonymous

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

60. anonymous

61. anonymous

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

62. anonymous

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

63. anonymous

ok, well, to be truthful...

64. anonymous

I never drink

65. anonymous

ever

66. 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?

67. anonymous

lol, good boy

68. anonymous

does it look fresh? does it smell funny?

69. anonymous

you are a good girl too

70. anonymous

oh you're all good

71. anonymous

^_^

72. anonymous

lol, so are you

73. anonymous

i think i'll cook it then go to bed

74. anonymous

you can cook?

75. anonymous

sorry to hijack the thread bmf

76. anonymous

not really. i push buttons on the microwave

77. anonymous

lol

78. anonymous

:)

79. anonymous

atleast that makes us all equal?

80. anonymous

and I ask my neighbour to cook food for me

81. anonymous

atleast I can cook an egg

82. anonymous

better than nothing lol ^_^

83. anonymous

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

84. 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

85. anonymous

oh lucky you, I just burn everything lol

86. anonymous

still learning :)

87. anonymous

:)

88. anonymous

89. anonymous

ok

90. anonymous

bye

91. anonymous

i;m out...bye

92. anonymous

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