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BecomeMyFan=D

  • 3 years ago

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

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

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

  3. sstarica
    • 3 years ago
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    or just factor?

  4. BecomeMyFan=D
    • 3 years ago
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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

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

  6. lokisan
    • 3 years ago
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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).

  7. sstarica
    • 3 years ago
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    how so?

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

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

  10. lokisan
    • 3 years ago
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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.

  11. lokisan
    • 3 years ago
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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.

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

  13. sstarica
    • 3 years ago
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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 :)

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

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

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

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

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

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

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

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

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

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

  24. sstarica
    • 3 years ago
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    great

  25. lokisan
    • 3 years ago
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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.

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

  27. lokisan
    • 3 years ago
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    yes

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

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

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

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

  32. BecomeMyFan=D
    • 3 years ago
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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

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

  34. lokisan
    • 3 years ago
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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.

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

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

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

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

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

  40. BecomeMyFan=D
    • 3 years ago
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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

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

  42. lokisan
    • 3 years ago
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    lol

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

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

  45. lokisan
    • 3 years ago
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    aw...

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

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

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

  49. sstarica
    • 3 years ago
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    still though.

  50. lokisan
    • 3 years ago
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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?

  51. sstarica
    • 3 years ago
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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

  52. lokisan
    • 3 years ago
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    cool

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

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

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

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

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

  58. sstarica
    • 3 years ago
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    exactly lol

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

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

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

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

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

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

  65. BecomeMyFan=D
    • 3 years ago
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    ever

  66. lokisan
    • 3 years ago
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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?

  67. sstarica
    • 3 years ago
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    lol, good boy

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

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

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

  71. sstarica
    • 3 years ago
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    ^_^

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

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

  74. sstarica
    • 3 years ago
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    you can cook?

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

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

  77. sstarica
    • 3 years ago
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    lol

  78. BecomeMyFan=D
    • 3 years ago
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    :)

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

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

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

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

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

  84. BecomeMyFan=D
    • 3 years ago
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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

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

  86. sstarica
    • 3 years ago
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    still learning :)

  87. BecomeMyFan=D
    • 3 years ago
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    :)

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

  89. BecomeMyFan=D
    • 3 years ago
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    ok

  90. sstarica
    • 3 years ago
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    bye

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

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

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