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B What are the applications of roots of a polynomial?

  1. Jul 1, 2017 #1
    Hello.

    Assume that I have two polynomials of degree 2, i.e., Quadratic Equations.

    1.
    Assume that the Quadratic Equation is:
    x2 + 7x + 12 = 0
    The roots of the Quadratic Equation is -3 and -4.

    2.
    Assume that there is another Quadratic Equation:
    x2 + 8x + 12 = 0
    The roots of the Quadratic Equation is -6 and -2.

    Then the use of the roots of the polynomial is that:
    When I am trying to find where two modeling equations intersect, where information overlaps, this is equivalent to finding the zeroes to know the difference of the models.
    The modeling equations I chose to consider is delineated as 1 and 2 above.

    What I think is, I find roots of two or more polynomials to know the differences between them or to do something else, like, initiating another curve from any of the roots.
    Am I right?
    I want to know the applications of a root of a polynomial.
    Do you have an example which illustrates use of a root of a polynomial?

    Thank you.
     
    Last edited: Jul 1, 2017
  2. jcsd
  3. Jul 1, 2017 #2

    BvU

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    Why don't you draw (sketch) the two parabolas ?

    Solving one of the quadratic equations gives you the (0, 1 or 2) points where they intersect the x-axis (i.e. where the quadratic form has value 0).

    Solving for the difference = 0 gives you possible intersection points. In this case the difference of the two forms reads x = 0
     
  4. Jul 1, 2017 #3
    From this statement, I think you confirmed that finding roots of a system of polynomials means finding the differences between those polynomials with respect to other polynomial.

    Right?
     
  5. Jul 1, 2017 #4

    BvU

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    The expression 'roots of polynomials' seems to confuse you.

    I don't know what you mean with 'finding roots of a system of polynomials'.

    What I do know is that you can try to find solutions for a system of equations.

    And I know what the roots of a single polynomial are.
     
  6. Jul 1, 2017 #5

    symbolipoint

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    pairofstrings

    You know something about roots of polynomial (or at least for quadratic) equations. You give a description more in line with finding the solution of a SYSTEM of quadratic equations.
    You are asking in effect, given x^2+7x+12=0 and x^2+8x+12=0, where do the FUNCTIONS which the left-hand members intersect?

    If that is what you are asking, then x^2+7x+12=x^2+8x+12.
    You can solve this. Subtract x^2 and 12, from both sides.
    7x=8x
    0=8x-7x
    0=x

    The two FUNCTIONS would seem to intersect at point (0,12).

    Keep studying and this will become clear (if not today, then sometime during Intermediate Algebra).
     
  7. Jul 1, 2017 #6
    Thanks for this information.
    I came to an answer to my original post.

    The root or zero or solution of an equation is the answer to the question.
    I find root, to get the answer to the question.

    'y' is a function in 'x'.
    y = f(x)

    So, to know 'x', I should make 'y' as nothing or zero.
    0 = f(x)
     
    Last edited: Jul 1, 2017
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