Help Finding Roots of Polynomial

  1. 1. The problem statement, all variables and given/known data
    First find all rational zeros of f, then use the depressed equation to find all roots of the equation f(x) = 0.
    f(x) = x^3 + 5x^2 - 8x + 2


    2. Relevant equations



    3. The attempt at a solution
    Possible rational zeros: 2, -2, 1, -1
    Synthetic division:

    1 | 1 5 -8 2
    _____1 6 -2
    =============
    1 6 -2 0

    Quotient: x^2 + 6x - 2
    Factored: (x + 3)^2 - 11

    I would think that the answer would just be x = -3 ± √(11) but the answer in the book says: {1, -3 ± √(11)}
    Where'd the 1 come from?
     
  2. jcsd
  3. rock.freak667

    rock.freak667 6,231
    Homework Helper

    Remember, you divided by (x-1), so your equation become (x-1)(x^2+6x-2)=0 -> x= 1 in addition to the other roots you found.
     
  4. Ohhhhhhh! I see now, thank you!
     
  5. synthetic division, oh lord
    if you want a nicer division algorithm try this

    or proper polynomial long division
    ... I really hated synthetic division :p
     
    Last edited by a moderator: Sep 25, 2014
  6. eumyang

    eumyang 1,347
    Homework Helper

    I believe we've had this discussion before, but there's nothing wrong with synthetic division. It's quick and pretty straightforward, IMO. Of course, if you're trying to divide a polynomial by a quadratic or a higher degree polynomial, then long division is the way to go.
     
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