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

1. BecomeMyFan=D Group Title

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

2. sstarica Group Title

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

3. sstarica Group Title

or just factor?

4. BecomeMyFan=D Group Title

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 Group Title

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

6. lokisan Group Title

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

7. sstarica Group Title

how so?

8. BecomeMyFan=D Group Title

yeah, how so?

9. lokisan Group Title

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 Group Title

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 Group Title

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 Group Title

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

13. sstarica Group Title

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 Group Title

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

15. lokisan Group Title

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

16. lokisan Group Title

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

17. sstarica Group Title

I think he fainted ._.

18. lokisan Group Title

lol you ok bmf?

19. sstarica Group Title

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

20. sstarica Group Title

more like in 5 steps? please?

21. BecomeMyFan=D Group Title

ok, just recovered

22. sstarica Group Title

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

23. BecomeMyFan=D Group Title

i am starting to understand the idea

24. sstarica Group Title

great

25. lokisan Group Title

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 Group Title

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

27. lokisan Group Title

yes

28. sstarica Group Title

okay, problema solved ^_^

29. lokisan Group Title

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

30. sstarica Group Title

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

31. lokisan Group Title

but that's easily handled - factor it out.

32. BecomeMyFan=D Group Title

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

33. BecomeMyFan=D Group Title

*but not nut

34. lokisan Group Title

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 Group Title

lol, thank you loki ^_^

36. lokisan Group Title

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

37. sstarica Group Title

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

38. sstarica Group Title

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

39. lokisan Group Title

with any luck...

40. BecomeMyFan=D Group Title

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 Group Title

i trust loki

42. lokisan Group Title

lol

43. sstarica Group Title

just your brain cells ._. LOL

44. sstarica Group Title

45. lokisan Group Title

aw...

46. sstarica Group Title

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

47. sstarica Group Title

well women too, but not as much though

48. sstarica Group Title

depends on the girl actually ^^"

49. sstarica Group Title

still though.

50. lokisan Group Title

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 Group Title

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 Group Title

cool

53. sstarica Group Title

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

54. sstarica Group Title

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

55. sstarica Group Title

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

56. sstarica Group Title

why ask such a question anyway?

57. BecomeMyFan=D Group Title

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

58. sstarica Group Title

exactly lol

59. sstarica Group Title

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

60. lokisan Group Title

61. sstarica Group Title

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

62. sstarica Group Title

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

63. BecomeMyFan=D Group Title

ok, well, to be truthful...

64. BecomeMyFan=D Group Title

I never drink

65. BecomeMyFan=D Group Title

ever

66. lokisan Group Title

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 Group Title

lol, good boy

68. sstarica Group Title

does it look fresh? does it smell funny?

69. BecomeMyFan=D Group Title

you are a good girl too

70. lokisan Group Title

oh you're all good

71. sstarica Group Title

^_^

72. sstarica Group Title

lol, so are you

73. lokisan Group Title

i think i'll cook it then go to bed

74. sstarica Group Title

you can cook?

75. lokisan Group Title

sorry to hijack the thread bmf

76. lokisan Group Title

not really. i push buttons on the microwave

77. sstarica Group Title

lol

78. BecomeMyFan=D Group Title

:)

79. sstarica Group Title

atleast that makes us all equal?

80. BecomeMyFan=D Group Title

and I ask my neighbour to cook food for me

81. sstarica Group Title

atleast I can cook an egg

82. sstarica Group Title

better than nothing lol ^_^

83. sstarica Group Title

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

84. BecomeMyFan=D Group Title

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 Group Title

oh lucky you, I just burn everything lol

86. sstarica Group Title

still learning :)

87. BecomeMyFan=D Group Title

:)

88. sstarica Group Title

89. BecomeMyFan=D Group Title

ok

90. sstarica Group Title

bye

91. lokisan Group Title

i;m out...bye

92. sammi789 Group Title

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