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Math Help - solve polynomial

  1. #1
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    solve polynomial

    Solve the equation: z^3 - 3z^2 + 6z -4=0

    Please Help!
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  2. #2
    Senior Member
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    Hi.

    Quote Originally Posted by gwiggy View Post
    Solve the equation: z^3 - 3z^2 + 6z -4=0

    Please Help!

    I guess you don't know newton's method to find zeros. Therefor you have to find a zero by guessing

    f(z) :=z^3 - 3z^2 + 6z -4

    very soon you find that f(1) = 1-3+6-4 = 0

    Then use polynomial long division to get

    [z^3-3z^2+6z-4] / [z-1] = z^2 - 2z + 4

    I guess you do know how to find the complex zeros of this polynom.

    Any questions?

    Regards,
    Rapha
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  3. #3
    MHF Contributor
    Joined
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    Talking

    Quote Originally Posted by gwiggy View Post
    Solve the equation: z^3 - 3z^2 + 6z -4=0
    Apply the Rational Roots Test to get a list of possible rational (integer or fraction) solutions: -4, -2, -1, 1, 2, and 4.

    Then apply long polynomial division or synthetic division to test each possible solution, and see which work. You may find it helpful to graph the related functon, f(x) = x^3 - 3x^2 + 6x - 4, in your calculator, so you can "see" which is the best possibility to check.

    Once you've found one solution, you'll be left with a quadratic, to which you can apply the Quadratic Formula.

    Have fun!
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