why are we interested in only those values of x for which y is zero?

Discussion in 'Math' started by PG1995, Nov 17, 2011.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi

    I understand that when roots a quadratic equation is found, we are essentially finding values of x for which y or f(x) is zero. But what how does it help us? I mean why are we only interested in values of x which makes y zero. e.g. quadratic formula for finding roots could only be used for finding values of x for which y is zero but it won't help us if we want to know values of x for which y is 2. Will it? Likewise, while solving differential equations we are only interested in those values which make the differential function equal to zero.

    [​IMG]

    Regards
    PG
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
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    The thing is, whenever you have a single variable equation that you need to solve, you can always rewrite it in the form f(x)=0.

    Let's say you had a quadratic 6x^2+2x+5=2. You can simply move the 2 to the other side and get 6x^2+2x+3=0

    Note that not all problems will result in a quadratic formula, but you can always get a form f(x)=0 to find x.
     
  3. endlessness

    New Member

    Apr 2, 2011
    1
    0
    Because any single-variable equation can be written as f(x)=0; then one can use root-finding algorithms to find a solution if it is not viable to find those numerically.
     
  4. justtrying

    Active Member

    Mar 9, 2011
    329
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    you use it to solve for all sorts of things...
     
  5. BillO

    Well-Known Member

    Nov 24, 2008
    985
    136
    Mathematically it's quite arbitrary. The answers here are all correct, but it could be anything. Y=2, y=2x-3 .. whatever. Just so long as the results are what you are after. Does this make sense? Just ask if not, but basically, what you are looking for is a relationship between two functions. So, in the end, it depends on the question being asked.
     
  6. sby64

    New Member

    Sep 29, 2012
    6
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    Although it may be too late to answer this question yet it may help someone. In my opinion and experience it is always good, easy and practical to get the reference point marked as zero from which you could easily calculate the direction (positive or negative) and the distance to reach your destination. In a two variable system you will be interested in all values of one variable that makes the other zero and unfortunately any value other than that will make life difficult due to a bad reference point. That is also precisely the reason why the reference in electrical/electronic circuit is considered to be at zero potential although it may actually not be truly at zero potential. But it makes life a lot easier.
     
  7. Wendy

    Moderator

    Mar 24, 2008
    20,765
    2,536
    Congratulations, you have practiced the arcane art of necromancy, the revival of a long dead thread. Likely the OP (Original Poster) has solved his problem in the years that has passed, or thrown it away, or something.

    It is usually a good idea to keep it within 6 months of the last post, unless it is your thread.
     
    tshuck likes this.
  8. DerStrom8

    Well-Known Member

    Feb 20, 2011
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  9. sby64

    New Member

    Sep 29, 2012
    6
    0
    Thanks for the good advice. Will follow that.
     
  10. WBahn

    Moderator

    Mar 31, 2012
    17,720
    4,788
    And, to cut a newbie a bit of slack, it is pretty easy to dredge up an old thread without realizing it. When you do a search (or when you try to start a new thread), the forum will present you with results its myopic little mind thinks are relevant. You seldom look at dates as you peruse(sp?) them and are apt to write a reply without thinking to do so. I suspect many of us have done it -- I know I have and more than once.

    If it hadn't been for Bill Marsden's note, I would have replied with a different reason why solving for roots is worthwhile, namely it allows you to factor a polynomial into a product of lower order polynomials, which can be quite useful.
     
    killivolt, justtrying and DerStrom8 like this.
  11. amilton542

    Active Member

    Nov 13, 2010
    494
    64
    On the contrary, I would just like to point out in that we're not always interested in certain solutions for a quadratic.

    For instance, solving trig' equations by means of the squaring method has a tendency to generate an extraneous solution that of which does not hold for the initial condition.
     
  12. Brownout

    Well-Known Member

    Jan 10, 2012
    2,375
    998

    Yeah, and that date is stinking hard to find. I've been on here for months, and I still have trouble finding it.
     
  13. killivolt

    Active Member

    Jan 10, 2010
    350
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    I don't care about whether or not it was right to pull it out of the Dead Thread Pile.

    It's one of those perfect things to read while eating lunch, short and sweet:rolleyes:
     
  14. electron_prince

    Member

    Sep 19, 2012
    93
    3
    you have a equation with a variable and you want to find value that value of variable which satisfies the equation. I mean you want to find that value of variable for which L.H.S = R.H.S. if we have zero on one side, it makes the work quite easy.
     
  15. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
    718
    This thread is a bump magnet, like a super-ball.
     
    DerStrom8 likes this.
  16. Brownout

    Well-Known Member

    Jan 10, 2012
    2,375
    998
    For what values of X is the bouncing super ball at Y=0?
     
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