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Quadratic Formula

  1. Nov 17, 2004 #1
    I know this is a basic question, but can someone please help me with WHEN to use the quadratic formula, i just wondered, can it be used on any quadratic???
  2. jcsd
  3. Nov 17, 2004 #2
    If a quadratic equation can be factorised then that is easier but you normally only use it when you can't factorise the quadratic and you want to know what x is.

    The Bob (2004 ©)
  4. Nov 17, 2004 #3
    thanks mate, just wonderin
  5. Nov 17, 2004 #4

    James R

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    You can use it whenever you want to solve for the roots (solutions) of an equation of the form:

    [tex]ax^2 + bx + c = 0[/tex]

    It works for any equation of this form. However, in some cases, it is unnecessary, as The Bob has already said. For example, if you have

    [tex]2x^2 + 4x - 6 = 0[/tex]

    this factorises to give

    [tex]2(x - 1)(x + 3) = 0[/tex],

    and you can see immediately that the solutions are x=1 or -3.
  6. Nov 17, 2004 #5


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    It's worth noting, I think, that the quadratic formula works on anything that can be expressed in quadratic form. For instance, if you have an equation like

    sin^2(x) + 2sin(x) - 2 = 0

    you can use the quadratic formula to solve for sin(x) - the equation is quadratic in sin(x).

    If you have an equation like

    x^4 - 3x^2 + 5 = 0

    you can use the quadratic formula to solve for x^2: the equation is quadratic in x^2. This last may be seen more easily if we use the substitution y = x^2: in that case, we have

    y^2 -3y + 5 = 0

    This is obviously a case where the quadratic formula applies. You use it to solve for y, then remember that y = x^2.

    There are a lot of places where this knowledge comes in very handy.
  7. Nov 17, 2004 #6
    The correct term is factor, not factorise.
  8. Nov 17, 2004 #7


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    You're speaking American. He's speaking English. :)
  9. Nov 17, 2004 #8
    Hmm, after some brief googling action, I think you're right. However, my claim was not baseless: I checked my Merriam-Webster's Dictionary, and factorise is not listed as a word, while factor is; one of the definitions is, of course, the mathematical one with which we are concerned here. It is an American dictionary, though, so I guess that explains it.
  10. Nov 18, 2004 #9
    for someone who knows history, how did the Neolithic use the quadratic equation?
    The Neolithic Age was before the first civilization.
  11. Nov 18, 2004 #10


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    If you mean the quadratic formula, they didn't. The Neolithic (New Stone) Age was before the development of formal mathematics.

    If you mean quadratics in general - again, they didn't. Same reason.

    If you mean situations inwhich quadratics are used today to describe them, then there were a lot. Quadratics, for instance, do a good job of describing the path a rock or a spear takes when thrown (if air resistance is neglected). I doubt, however, that someone without a written language would be capable of, or for that matter need to, solve something like that to catch dinner.
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