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How to find the roots of polynomial of a 5.th order

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data
    I have a polynimal equation as this
    - 0.00000000000049125*T^4 + 0.00000000021358333333333333333333333333333*T^3 + 0.00000290233125*T^2 - 0.032444109375*T + 19.891472013020833333333333333333



    2. Relevant equations



    3. The attempt at a solution

    I insert those polynomial coeffictions to an line matris
    a = [- 0.00000000000049125 0.00000000021358333333333333333333333333333 0.00000290233125 - 0.032444109375 19.891472013020833333333333333333]

    a =
    -0.0000 0.0000 0.0000 0.0324 19.8915
    and call roots function with thi array
    roots(a)

    and get this values

    ans =

    1.0e+003 *

    4.8369
    -1.8781 + 3.0710i
    -1.8781 - 3.0710i
    -0.6460

    I seen, there are real and complex roots. So, How can I find real value of T ??
    Should I use a method like bisection ? If so how ?
     
  2. jcsd
  3. Jan 17, 2012 #2

    Curious3141

    User Avatar
    Homework Helper

    First of all, your equation is not 5th "order" (proper term is degree), it's only 4th degree (also called a quartic equation).

    There are at most 4 distinct roots to any quartic with rational coefficients (like you have). These roots can be found exactly with certain algebraic operations, but it's fairly tedious. You've apparently already run the equation through a solver and got those roots.

    So you have two distinct real roots and two complex roots (the ones with 'i' in them), to give a total of 4 roots. If you only need the real roots, just use those (so T can be either of those values). Just ignore the complex roots unless you have a problem where you need to use those (and you have some means to interpret a complex solution).
     
  4. Jan 17, 2012 #3
    Thanks for the valuable information.

    I tried this online polynomail root solver and entered the polnomial coefficients,
    and the these results.

    Instead of 1.0e+003 *

    4.8369

    I get
    4836.92716144589

    and others are
    x2:
    -646.021532813122

    x3:
    -1878.065197692127 + 3071.020155085326i

    x4:
    -1878.065197692127 - 3071.020155085326i

    . I get confused at this point, I can not fully understand "e" concept here, I know it means exponential but I do not know how can I calculate real value of a number which contains that "e" sign.

    I mean, in this case
    1.0e+003 *

    4.8369

    is equals to 4836.92716144589 ??

    Which numebr should I accepts, can you also help me on this ?
     
    Last edited: Jan 17, 2012
  5. Jan 17, 2012 #4

    Curious3141

    User Avatar
    Homework Helper

    1e3 means 1000 here. The '*' means times (multiply). The first solver was factoring out the 1000, so that the numbers appear smaller. You're meant to take 1000 times each number to get the actual solution.

    The second solver just gave the solutions as is.

    "x"e"y" also written as xEy or xEXPy (that's why some scientific calcs have that "EXP" key, which means the same thing) where x and y are numbers (generally x is a single digit number greater than or equal to 1 and less than 10 and y can be anything, positive or negative) means x TIMES 10^y.

    So 2e4 = 20,000. and 3e-6 = 3/1,000,000.

    It's a form of Scientific Notation: http://en.wikipedia.org/wiki/Scientific_notation
     
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