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anonymous

  • 5 years ago

Is it true that for a quadratic equation ax^2+bx+c, the roots of the equation will always equal -b/a?

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  1. amistre64
    • 5 years ago
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    nope

  2. amistre64
    • 5 years ago
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    -b/a aint even an option...unless you get real lucky lol

  3. myininaya
    • 5 years ago
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    it will always be x=frac{-b pm sqrt{b^2-4ac}{2a} a does not equal zero

  4. myininaya
    • 5 years ago
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    that didn't work

  5. anonymous
    • 5 years ago
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    There is a sort of cheat way to factor it though. I'm told it's not technically mathematically sound, but I like it and it works. Multiply a and b

  6. amistre64
    • 5 years ago
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    lol....its the french version

  7. amistre64
    • 5 years ago
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    that only works for integer roots

  8. anonymous
    • 5 years ago
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    Then no wonder it's not mathematically sound. Ahaha

  9. amistre64
    • 5 years ago
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    well, for roots that dont incvolve radicals

  10. anonymous
    • 5 years ago
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    And no, not really. You just gotta tweak it.

  11. anonymous
    • 5 years ago
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    so it will equal -b/a, assuming I'm only working with integers?

  12. myininaya
    • 5 years ago
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    \[x=\frac\]

  13. amistre64
    • 5 years ago
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    no.....-b/a aint even on the board

  14. anonymous
    • 5 years ago
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    but i keep trying to find a counterexample and cant

  15. amistre64
    • 5 years ago
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    -b/2a is a possibility; but that aint always a root unless the graph just touches once

  16. amistre64
    • 5 years ago
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    if its a complete square than -b/2a ia the only root

  17. anonymous
    • 5 years ago
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    -b/2a is to find the vertex...

  18. anonymous
    • 5 years ago
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    i just want to find a counterexample to -b/a being the sum of the roots

  19. amistre64
    • 5 years ago
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    -b/2a is the axis of symmetry; but its also half way between roots :)

  20. anonymous
    • 5 years ago
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    my bad, i forgot to mention sum

  21. amistre64
    • 5 years ago
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    if its a complete square than -b/2a ia the only root

  22. amistre64
    • 5 years ago
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    that was weird lol

  23. myininaya
    • 5 years ago
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    so you want to find a counterexample: how about x^2-5x+6=0 -b/a=5 but there are two solutions and neither of them are 5 the solutions are x=3 and x=2

  24. anonymous
    • 5 years ago
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    3+2=5, forgot to mention that the sum of the roots = -b/a

  25. myininaya
    • 5 years ago
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    oh ok

  26. amistre64
    • 5 years ago
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    the quad formula says; stand in the middle at -b/2a....now look left and right an equal distance of sqrt(...)/2a

  27. myininaya
    • 5 years ago
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    i have a proof

  28. anonymous
    • 5 years ago
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    ?

  29. myininaya
    • 5 years ago
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  30. anonymous
    • 5 years ago
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    lol, did you just do that?

  31. myininaya
    • 5 years ago
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    yes does it make sense?

  32. anonymous
    • 5 years ago
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    yea, do you know how it can be useful though?

  33. myininaya
    • 5 years ago
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    you can use it to sort of check yourself instead of plugging your answers back into the equation to check you can just see they add up to be -b/a thanks for pointing this out i never realized it before

  34. anonymous
    • 5 years ago
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    lol, your welcome XD

  35. myininaya
    • 5 years ago
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    the square roots cancel because one was postive and one was negative just like 5+(-5)=0 so you completely understand? thats amazing well unless you are passed algebra by now

  36. anonymous
    • 5 years ago
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    I am. My sis just brought this to my attention and I never realized it before. XD

  37. myininaya
    • 5 years ago
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    its really cool :)

  38. myininaya
    • 5 years ago
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    by way it works for all numbers

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