College Algebra

Directions: Find the REAL solutions of the equation

x^3-2.6x^2=3.93


Please help, its for my final!

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  1. I don't like decimals ,so multiply each term by 100

    100x^3 - 260x^2 = 393
    100x^3 - 260x^2 - 393 = 0

    I don't know what level of math this is, but there is no simple algebraic way to solve this cubic.
    I tried the usual
    f(1), f(-1), f(3), etc to find a zero but nothing there.

    I finally tried my trusty on line cubic equation solver
    http://www.1728.com/cubic.htm
    and found one real root, with 2 complex roots tossed in.

    Have you been given some cubic equation formula?
    This would be a very unlikely equation for a final.

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    posted by Reiny
  2. No. I swear its on my final for college algebra.

    I know the answer is 3.028

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    posted by Courtney
  3. Are you familiar with Newton's Method perhaps?

    xnew = xold - f(old)/ f ' (old)

    let f(x) = 100x^3 - 260x^2 - 393
    f '(x) = 300x^2 - 520x

    guess at old = 3 (the graph showed an x -intercept at around 3)

    old --- new
    3 ....... 3.02895
    3.02895 3.02849
    3.02849 3.02849 same answer to 5 decimals

    no matter what you pick as your first "old" it will eventually close in on that answer, it will just take more steps.
    The closer your first guess, the faster the process.

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    posted by Reiny

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