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Hello, need help with quadratic equation

  1. Feb 28, 2013 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations

    x(2x^2 - 5) = -1

    3. The attempt at a solution

    This question has been flung at me without any pre-examples how to solve it. I have only dealt with equations like 2x^2 + 5x - 12 = 0. I know that the equation above should be set to zero, but how do I deal with the x coefficient on the paranthesis?

    I don't know how to solve this -- it's very confusing and if someone can help me I would be grateful!
     
  2. jcsd
  3. Feb 28, 2013 #2
    I know I need to factorize which is my problem, I am not sure how to when there is an x outside the paramnthesis?
     
  4. Feb 28, 2013 #3

    eumyang

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    Homework Helper

    Well, the first thing is that this is not a quadratic equation. It is a cubic. Second, when solving polynomial equations, I would first remove all parentheses (by using the distributive law or by multiplying out) and then collect all terms to the left side. Only then would I try to factor, if possible.
     
  5. Feb 28, 2013 #4
    Do you think there has been a mistake then because the unit I am on is [specifically] quadratic equations? No wonder I wasn't sure about it.... If I multiply it out I get

    2x^3 - 5x = -1

    and then

    2x^3 - 5x + 1 = 0

    right?
     
  6. Feb 28, 2013 #5
    So how do I factor that? I've never factored a cubic equation...
     
  7. Feb 28, 2013 #6

    eumyang

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    Yes, the work is correct. Is this problem from a book? There are three solutions, none of which are rational, so I wonder if there was a typo somewhere.
     
  8. Feb 28, 2013 #7
    It does actually say, make correct to the first decimal place...?
     
  9. Feb 28, 2013 #8
    and yes, problem from a book... odd to find a cubic equation in the quadratic section...
     
  10. Feb 28, 2013 #9
    will you plz show me how to solve this?
     
  11. Feb 28, 2013 #10

    eumyang

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    This is not solvable by factoring. All three roots are irrational, so that means you cannot use the Rational Roots Theorem either. You could just graph it on a graphing calculator and have it find the solutions for you.

    There exists a cubic formula, but it is overly complicated to use, and it is not taught AFAIK in courses in elementary/intermediate algebra or precalculus.
     
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