## BecomeMyFan=D 4 years ago Calculate the sum and the product of the equation roots. Give the answer in fractions (ex: x = 3 ¾).

1. BecomeMyFan=D

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

2. sstarica

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

3. sstarica

or just factor?

4. BecomeMyFan=D

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. lokisan

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

6. lokisan

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

7. sstarica

how so?

8. BecomeMyFan=D

yeah, how so?

9. lokisan

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. lokisan

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. lokisan

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. BecomeMyFan=D

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

13. sstarica

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. lokisan

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

15. lokisan

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

16. lokisan

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

17. sstarica

I think he fainted ._.

18. lokisan

lol you ok bmf?

19. sstarica

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

20. sstarica

more like in 5 steps? please?

21. BecomeMyFan=D

ok, just recovered

22. sstarica

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

23. BecomeMyFan=D

i am starting to understand the idea

24. sstarica

great

25. lokisan

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. sstarica

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

27. lokisan

yes

28. sstarica

okay, problema solved ^_^

29. lokisan

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

30. sstarica

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

31. lokisan

but that's easily handled - factor it out.

32. BecomeMyFan=D

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

33. BecomeMyFan=D

*but not nut

34. lokisan

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. sstarica

lol, thank you loki ^_^

36. lokisan

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

37. sstarica

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

38. sstarica

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

39. lokisan

with any luck...

40. BecomeMyFan=D

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. BecomeMyFan=D

i trust loki

42. lokisan

lol

43. sstarica

just your brain cells ._. LOL

44. sstarica

45. lokisan

aw...

46. sstarica

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

47. sstarica

well women too, but not as much though

48. sstarica

depends on the girl actually ^^"

49. sstarica

still though.

50. lokisan

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. sstarica

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. lokisan

cool

53. sstarica

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

54. sstarica

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

55. sstarica

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

56. sstarica

why ask such a question anyway?

57. BecomeMyFan=D

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

58. sstarica

exactly lol

59. sstarica

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

60. lokisan

61. sstarica

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

62. sstarica

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

63. BecomeMyFan=D

ok, well, to be truthful...

64. BecomeMyFan=D

I never drink

65. BecomeMyFan=D

ever

66. lokisan

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. sstarica

lol, good boy

68. sstarica

does it look fresh? does it smell funny?

69. BecomeMyFan=D

you are a good girl too

70. lokisan

oh you're all good

71. sstarica

^_^

72. sstarica

lol, so are you

73. lokisan

i think i'll cook it then go to bed

74. sstarica

you can cook?

75. lokisan

sorry to hijack the thread bmf

76. lokisan

not really. i push buttons on the microwave

77. sstarica

lol

78. BecomeMyFan=D

:)

79. sstarica

atleast that makes us all equal?

80. BecomeMyFan=D

and I ask my neighbour to cook food for me

81. sstarica

atleast I can cook an egg

82. sstarica

better than nothing lol ^_^

83. sstarica

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

84. BecomeMyFan=D

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. sstarica

oh lucky you, I just burn everything lol

86. sstarica

still learning :)

87. BecomeMyFan=D

:)

88. sstarica

89. BecomeMyFan=D

ok

90. sstarica

bye

91. lokisan

i;m out...bye

92. sammi789

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