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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

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  1. BecomeMyFan=D
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    \[-3x ^{2}+2x+4=0\]

    • 3 years ago
  2. sstarica
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    do you want to find the answer when you plug x in the equation?

    • 3 years ago
  3. sstarica
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    or just factor?

    • 3 years ago
  4. BecomeMyFan=D
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    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

    • 3 years ago
  5. lokisan
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    It wants you to understand the relationship between the roots and coefficients in a quadratic.

    • 3 years ago
  6. lokisan
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    If you do, you can read off from that equation what you need to know without any working (well, much working).

    • 3 years ago
  7. sstarica
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    how so?

    • 3 years ago
  8. BecomeMyFan=D
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    yeah, how so?

    • 3 years ago
  9. lokisan
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    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\[c={\alpha}{\beta}\]

    • 3 years ago
  10. lokisan
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    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.

    • 3 years ago
  11. lokisan
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    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.

    • 3 years ago
  12. BecomeMyFan=D
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    ok.... *eyes wide open, helpless face*

    • 3 years ago
  13. sstarica
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    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 :)

    • 3 years ago
  14. lokisan
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    \[-3x^2+2x+4=0 \iff x^2-\frac{2}{3}x-\frac{4}{3}=0\]

    • 3 years ago
  15. lokisan
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    Then you can read off the sum and product of roots.

    • 3 years ago
  16. lokisan
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    \[\alpha + \beta = \frac{2}{3}\]\[{\alpha}{\beta}=-\frac{4}{3}\]

    • 3 years ago
  17. sstarica
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    I think he fainted ._.

    • 3 years ago
  18. lokisan
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    lol you ok bmf?

    • 3 years ago
  19. sstarica
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    loki what were you trying to say, can you summarize it please? :)

    • 3 years ago
  20. sstarica
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    more like in 5 steps? please?

    • 3 years ago
  21. BecomeMyFan=D
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    ok, just recovered

    • 3 years ago
  22. sstarica
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    lol, he'll summarize it don't worry ^_^

    • 3 years ago
  23. BecomeMyFan=D
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    i am starting to understand the idea

    • 3 years ago
  24. sstarica
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    great

    • 3 years ago
  25. lokisan
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    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.

    • 3 years ago
  26. sstarica
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    so now he can put them equal to each other and continue.

    • 3 years ago
  27. lokisan
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    yes

    • 3 years ago
  28. sstarica
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    okay, problema solved ^_^

    • 3 years ago
  29. lokisan
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    the only catch is that you have to ensure the coefficient of x^2 is 1.

    • 3 years ago
  30. sstarica
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    he'll divide by -3 like you've said , got that andy?

    • 3 years ago
  31. lokisan
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    but that's easily handled - factor it out.

    • 3 years ago
  32. BecomeMyFan=D
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    ok, got it, nut I think I have to get drunk like loki so next time I can figure stuff faster

    • 3 years ago
  33. BecomeMyFan=D
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    *but not nut

    • 3 years ago
  34. lokisan
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    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.

    • 3 years ago
  35. sstarica
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    lol, thank you loki ^_^

    • 3 years ago
  36. lokisan
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    yeah, have a beer and mathematics will be more fun ;)

    • 3 years ago
  37. sstarica
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    you don't need to get drunk to answer a question andrius

    • 3 years ago
  38. sstarica
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    lol so he'll get 4 when you ask him 1+1 ._.

    • 3 years ago
  39. lokisan
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    with any luck...

    • 3 years ago
  40. BecomeMyFan=D
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    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

    • 3 years ago
  41. BecomeMyFan=D
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    i trust loki

    • 3 years ago
  42. lokisan
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    lol

    • 3 years ago
  43. sstarica
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    just your brain cells ._. LOL

    • 3 years ago
  44. sstarica
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    drinking is bad bad bad, but you boys are just so stubborn to accept that.

    • 3 years ago
  45. lokisan
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    aw...

    • 3 years ago
  46. sstarica
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    I'm serious, men always do the opposite lol, wanting to try everything

    • 3 years ago
  47. sstarica
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    well women too, but not as much though

    • 3 years ago
  48. sstarica
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    depends on the girl actually ^^"

    • 3 years ago
  49. sstarica
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    still though.

    • 3 years ago
  50. lokisan
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    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?

    • 3 years ago
  51. sstarica
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    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

    • 3 years ago
  52. lokisan
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    cool

    • 3 years ago
  53. sstarica
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    wait, if the weather's cold, then I guess it's safe

    • 3 years ago
  54. sstarica
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    it'll keep the chicken cooled just like leaving it in a fridge.

    • 3 years ago
  55. sstarica
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    there's no difference, the only small difference is temperature and where you place it.

    • 3 years ago
  56. sstarica
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    why ask such a question anyway?

    • 3 years ago
  57. BecomeMyFan=D
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    I am kind of lost on how beer, chikens and men wanting to do the opposite relate to each other

    • 3 years ago
  58. sstarica
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    exactly lol

    • 3 years ago
  59. sstarica
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    see what happens when you drink? you lose the relation between subjects and things.

    • 3 years ago
  60. lokisan
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    lol...sad

    • 3 years ago
  61. sstarica
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    evidence = loki's question , no more drinking for you

    • 3 years ago
  62. sstarica
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    but he has a point, what does that question got to do with drinking?

    • 3 years ago
  63. BecomeMyFan=D
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    ok, well, to be truthful...

    • 3 years ago
  64. BecomeMyFan=D
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    I never drink

    • 3 years ago
  65. BecomeMyFan=D
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    ever

    • 3 years ago
  66. lokisan
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    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?

    • 3 years ago
  67. sstarica
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    lol, good boy

    • 3 years ago
  68. sstarica
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    does it look fresh? does it smell funny?

    • 3 years ago
  69. BecomeMyFan=D
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    you are a good girl too

    • 3 years ago
  70. lokisan
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    oh you're all good

    • 3 years ago
  71. sstarica
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    ^_^

    • 3 years ago
  72. sstarica
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    lol, so are you

    • 3 years ago
  73. lokisan
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    i think i'll cook it then go to bed

    • 3 years ago
  74. sstarica
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    you can cook?

    • 3 years ago
  75. lokisan
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    sorry to hijack the thread bmf

    • 3 years ago
  76. lokisan
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    not really. i push buttons on the microwave

    • 3 years ago
  77. sstarica
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    lol

    • 3 years ago
  78. BecomeMyFan=D
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    :)

    • 3 years ago
  79. sstarica
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    atleast that makes us all equal?

    • 3 years ago
  80. BecomeMyFan=D
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    and I ask my neighbour to cook food for me

    • 3 years ago
  81. sstarica
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    atleast I can cook an egg

    • 3 years ago
  82. sstarica
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    better than nothing lol ^_^

    • 3 years ago
  83. sstarica
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    though I'm still learning, I want to >_<

    • 3 years ago
  84. BecomeMyFan=D
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    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

    • 3 years ago
  85. sstarica
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    oh lucky you, I just burn everything lol

    • 3 years ago
  86. sstarica
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    still learning :)

    • 3 years ago
  87. BecomeMyFan=D
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    :)

    • 3 years ago
  88. sstarica
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    anyways, basket time, talk later

    • 3 years ago
  89. BecomeMyFan=D
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    ok

    • 3 years ago
  90. sstarica
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    bye

    • 3 years ago
  91. lokisan
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    i;m out...bye

    • 3 years ago
  92. sammi789
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    Try www.aceyourcollegeclasses.com

    • 3 years ago
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